{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 5, m: 7} to form a word, what is the expected number of matches of the pattern 'mk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 2, f: 4, s: 2, z: 2, i: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 2, v: 1, y: 2, z: 5, n: 2} to form a word, what is the expected number of matches of the pattern 'zy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 1, a: 3, l: 3, e: 5} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 2, t: 1, k: 2, d: 7} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 5, u: 4, p: 3}. What is the expected number of occurrences of the pattern 'p*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 2, s: 4, v: 3, w: 3}, what is the expected number of times the pattern 'sv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 2, f: 2, o: 2, k: 3, b: 3}, what is the expected number of times the pattern 'k*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 5, q: 2, w: 2, u: 3}. What is the expected number of occurrences of the pattern 'cw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, m: 9}. What is the expected number of occurrences of the pattern 'x+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 4, w: 4, i: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'h*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 8, t: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 1, x: 3, r: 4, i: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 5, r: 7}, what is the expected number of times the pattern 'rc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 2, e: 3, c: 2, r: 3, q: 2}. What is the expected number of occurrences of the pattern 'ec+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, h: 4, x: 2, q: 2, j: 1}. What is the expected number of occurrences of the pattern 'k.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 4, p: 2, c: 3, n: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 5, x: 7} to form a word, what is the expected number of matches of the pattern 'xg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 5, v: 1, r: 3, k: 3}, what is the expected number of times the pattern 'kt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, z: 3, k: 2, i: 1, d: 3}. What is the expected number of occurrences of the pattern 'k.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 3, u: 9} to form a word, what is the expected number of matches of the pattern 'u+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, m: 2, a: 4, e: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 5, l: 2, z: 5} to form a word, what is the expected number of matches of the pattern 'zl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 2, l: 5, u: 2, g: 3}, what is the expected number of times the pattern 'sl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.54", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 8, u: 4} to form a word, what is the expected number of matches of the pattern 'du*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 3, g: 1, t: 3, l: 5}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, w: 9}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, p: 4, f: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 4, q: 3, y: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 5, b: 3, a: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 5, v: 7}. What is the expected number of occurrences of the pattern 'w.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 2, z: 3, t: 3, d: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 7, j: 5}. What is the expected number of occurrences of the pattern 'j.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 7, o: 5} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 6, t: 6} to form a word, what is the expected number of matches of the pattern 'v+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 2, e: 2, k: 3, b: 5}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 8, c: 2, s: 2}. What is the expected number of occurrences of the pattern 'ps*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 3, o: 2, d: 4, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 2, h: 2, w: 4, k: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, d: 2, q: 6, b: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 8, t: 4}, what is the expected number of times the pattern 'y.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, w: 5, j: 4}, what is the expected number of times the pattern 'c*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 5, y: 4, d: 2, z: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, e: 3, m: 4}, what is the expected number of times the pattern 'm+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 2, v: 1, k: 4, o: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 1, x: 2, w: 4, i: 3, y: 2}, what is the expected number of times the pattern 'w.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 2, o: 6, c: 4}. What is the expected number of occurrences of the pattern 'o*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 5, v: 7} to form a word, what is the expected number of matches of the pattern 'v*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 3, t: 5, s: 2, m: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 3, c: 3, j: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'kc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 3, g: 3, h: 4, j: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'h+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 1, f: 1, y: 4, u: 3, k: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 7, z: 5}. What is the expected number of occurrences of the pattern 'zm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 2, f: 3, i: 3, u: 4}, what is the expected number of times the pattern 'w+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 4, t: 2, d: 1, q: 3, g: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 1, s: 4, a: 1, i: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 5, s: 2, m: 5}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 7, i: 5}. What is the expected number of occurrences of the pattern 'i*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 2, k: 6, u: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, k: 2, y: 7}. What is the expected number of occurrences of the pattern 'q.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 4, s: 5, l: 1, r: 2}. What is the expected number of occurrences of the pattern 'l*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.69", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 7, m: 5}, what is the expected number of times the pattern 'm.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, l: 3, k: 3, n: 3}. What is the expected number of occurrences of the pattern 'k.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 5, m: 4, l: 3}. What is the expected number of occurrences of the pattern 'lc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {u: 6, v: 6} to form a word, what is the expected number of matches of the pattern 'u+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, e: 6, p: 3, r: 1}. What is the expected number of occurrences of the pattern 'p+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 1, s: 5, c: 2, i: 2, r: 2}, what is the expected number of times the pattern 'r+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, l: 6, m: 4}. What is the expected number of occurrences of the pattern 'l.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 6, n: 6}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, s: 7, t: 3}. What is the expected number of occurrences of the pattern 't*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 4, r: 2, l: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'lt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 2, m: 4, b: 2, l: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'o+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, x: 5, c: 4}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 2, f: 3, j: 1, w: 3, r: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 3, f: 5, w: 4} to form a word, what is the expected number of matches of the pattern 'w+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 6, o: 6}, what is the expected number of times the pattern 'zo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 2, c: 1, t: 6, l: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 2, r: 3, e: 6, q: 1}, what is the expected number of times the pattern 'e*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, b: 1, c: 3, g: 3, r: 3}. What is the expected number of occurrences of the pattern 'r+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 6, l: 6}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 3, s: 3, v: 3, u: 3}, what is the expected number of times the pattern 'v.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 4, u: 1, w: 2, z: 1, k: 4}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 4, t: 2, e: 3, d: 3}. What is the expected number of occurrences of the pattern 'he*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 5, n: 2, f: 5} to form a word, what is the expected number of matches of the pattern 'g.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 2, p: 1, n: 3, c: 1, w: 5}, what is the expected number of times the pattern 'wp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.69", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 2, s: 5, d: 3, w: 2}. What is the expected number of occurrences of the pattern 'w+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 1, r: 2, c: 3, w: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'l.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 7, s: 5}. What is the expected number of occurrences of the pattern 's+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 7, u: 5} to form a word, what is the expected number of matches of the pattern 's.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 3, f: 6, p: 3}. What is the expected number of occurrences of the pattern 'n.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, h: 5, i: 4}, what is the expected number of times the pattern 'h*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 7, y: 5} to form a word, what is the expected number of matches of the pattern 'ry+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 3, l: 9} to form a word, what is the expected number of matches of the pattern 'a.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 1, j: 4, l: 3, t: 3, n: 1}, what is the expected number of times the pattern 'nl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 3, h: 3, g: 6}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 4, x: 5, h: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 4, m: 5, e: 2, r: 1}. What is the expected number of occurrences of the pattern 'p.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 1, p: 4, i: 2, o: 1, a: 4}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 7, v: 5}, what is the expected number of times the pattern 'y*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 5, b: 7}. What is the expected number of occurrences of the pattern 'vv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 9, h: 3}. What is the expected number of occurrences of the pattern 'eh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, b: 2, u: 3, h: 3}. What is the expected number of occurrences of the pattern 'u+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 4, v: 2, o: 3, c: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 8, p: 2, c: 2}. What is the expected number of occurrences of the pattern 'z+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 1, g: 1, q: 4, t: 3, k: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, f: 3, j: 2, e: 4}. What is the expected number of occurrences of the pattern 'e.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 2, s: 7, q: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 3, l: 3, c: 2, y: 2, q: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 9, s: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 1, t: 2, y: 3, l: 4, s: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 4, b: 1, f: 4, z: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 6, f: 6} to form a word, what is the expected number of matches of the pattern 'if*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 3, e: 2, d: 1, g: 4, u: 2}. What is the expected number of occurrences of the pattern 'd.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, v: 8}, what is the expected number of times the pattern 'i+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 1, m: 4, s: 1, b: 3, c: 3}, what is the expected number of times the pattern 'zm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 2, o: 4, v: 4, m: 2}. What is the expected number of occurrences of the pattern 'o*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 6, d: 6} to form a word, what is the expected number of matches of the pattern 'd*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 6, r: 2, m: 4}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 5, i: 2, g: 3, r: 2} to form a word, what is the expected number of matches of the pattern 'ri*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 3, w: 2, e: 2, t: 5}. What is the expected number of occurrences of the pattern 'ew*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 5, c: 4, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 2, f: 1, l: 4, q: 5}, what is the expected number of times the pattern 'fq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 4, l: 5, a: 1, e: 2}. What is the expected number of occurrences of the pattern 'l+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 3, y: 6, b: 3}. What is the expected number of occurrences of the pattern 'n*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 7, e: 5}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 2, s: 1, h: 3, g: 3, i: 3}, what is the expected number of times the pattern 'gs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, x: 5, w: 2, t: 3}. What is the expected number of occurrences of the pattern 't+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 3, v: 4, d: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'zd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 5, k: 4, g: 3}, what is the expected number of times the pattern 'k+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 4, z: 2, y: 3, e: 3}, what is the expected number of times the pattern 'ye*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, g: 5, t: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 5, l: 3, d: 4} to form a word, what is the expected number of matches of the pattern 'fl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 5, p: 3, h: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'h*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 2, d: 1, a: 3, r: 4, z: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 3, o: 4, y: 5}, what is the expected number of times the pattern 'oi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 2, d: 3, b: 5, y: 2}, what is the expected number of times the pattern 'y*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 3, i: 5, l: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'vs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 7, k: 5} to form a word, what is the expected number of matches of the pattern 'ak*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 8, t: 4}, what is the expected number of times the pattern 'i+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 10, v: 2} to form a word, what is the expected number of matches of the pattern 'o+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.97", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, j: 4, u: 3, y: 2}, what is the expected number of times the pattern 'y.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 3, u: 2, y: 4, z: 3}. What is the expected number of occurrences of the pattern 'z*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 1, w: 1, x: 4, k: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 4, s: 3, y: 1, r: 4} to form a word, what is the expected number of matches of the pattern 'r*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 4, w: 3, m: 5} to form a word, what is the expected number of matches of the pattern 'w.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, t: 2, y: 5, s: 1, v: 1}, what is the expected number of times the pattern 'y.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 6, x: 6} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 3, s: 9}. What is the expected number of occurrences of the pattern 'c+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 8, y: 4} to form a word, what is the expected number of matches of the pattern 'w*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 6, m: 6} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 2, k: 2, w: 4, g: 2, t: 2}. What is the expected number of occurrences of the pattern 'vw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 1, f: 3, c: 3, h: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'f+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 3, l: 4, t: 2, n: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 3, z: 7, f: 2}. What is the expected number of occurrences of the pattern 'f.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.59", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, z: 1, j: 4, w: 3, g: 1}. What is the expected number of occurrences of the pattern 'g+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 6, h: 6} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 2, y: 1, z: 3, h: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'y.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, o: 3, g: 6}, what is the expected number of times the pattern 'og+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 3, g: 2, j: 6, v: 1} to form a word, what is the expected number of matches of the pattern 'g+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 1, j: 2, z: 3, b: 1, r: 5}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, s: 4, w: 2, r: 1, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, a: 1, c: 3, i: 5}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 8, m: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 5, h: 7} to form a word, what is the expected number of matches of the pattern 'h.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 7, q: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'qb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 3, n: 4, d: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'ne+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 6, r: 4, w: 2}, what is the expected number of times the pattern 'lr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 1, f: 2, j: 4, d: 2, v: 3}, what is the expected number of times the pattern 'df*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 1, z: 4, i: 4, s: 3}. What is the expected number of occurrences of the pattern 's*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 4, y: 2, e: 6}. What is the expected number of occurrences of the pattern 'y.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 2, j: 2, t: 4, n: 4}. What is the expected number of occurrences of the pattern 'j+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 3, f: 2, y: 1, e: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 3, a: 2, q: 4, p: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 2, t: 1, v: 4, q: 2, f: 3}, what is the expected number of times the pattern 'ft+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, d: 9}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, g: 4, e: 2, x: 4}. What is the expected number of occurrences of the pattern 'x.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 4, t: 3, s: 2, l: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 5, b: 5, q: 2} to form a word, what is the expected number of matches of the pattern 'qz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.54", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 3, b: 1, y: 2, u: 3, s: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 2, j: 3, z: 4, q: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 8, l: 4}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 2, k: 4, s: 1, l: 1, g: 4} to form a word, what is the expected number of matches of the pattern 'sk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 2, y: 3, q: 2, s: 1, v: 4}. What is the expected number of occurrences of the pattern 'sy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 4, g: 4, x: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'do+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, d: 3, i: 2, c: 2, f: 3}. What is the expected number of occurrences of the pattern 'o+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 2, r: 3, p: 2, v: 2, n: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 5, t: 7}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 4, l: 2, n: 2, m: 3, z: 1}. What is the expected number of occurrences of the pattern 'z*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 7, l: 5}. What is the expected number of occurrences of the pattern 'ml+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 2, e: 1, v: 2, x: 4, r: 3} to form a word, what is the expected number of matches of the pattern 'ev+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 4, p: 4, u: 1, s: 1, w: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 5, m: 1, v: 3, n: 1, i: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 2, e: 4, z: 6}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, p: 3, y: 2, h: 1, x: 3}, what is the expected number of times the pattern 'yx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 2, z: 3, a: 2, t: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 2, v: 5, q: 3, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 7, h: 5}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 2, m: 3, w: 3, g: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'mn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 2, u: 7, z: 3}, what is the expected number of times the pattern 'h.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 7, z: 5} to form a word, what is the expected number of matches of the pattern 'q.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 4, m: 2, r: 2, w: 4}. What is the expected number of occurrences of the pattern 'rv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 4, o: 5, r: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 3, z: 2, q: 2, s: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'q*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 2, b: 7, a: 3}. What is the expected number of occurrences of the pattern 'a*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 3, f: 4, t: 5} to form a word, what is the expected number of matches of the pattern 'th*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 5, x: 7}, what is the expected number of times the pattern 'x*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 3, s: 2, f: 4, a: 3} to form a word, what is the expected number of matches of the pattern 'sa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 3, y: 5, u: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 5, y: 4, a: 3} to form a word, what is the expected number of matches of the pattern 'g*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 2, y: 2, s: 4, h: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'mh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 5, c: 2, o: 1, e: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 7, p: 3, r: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 6, j: 6}. What is the expected number of occurrences of the pattern 'ja*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 1, p: 3, l: 4, t: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'm*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 6, h: 2, k: 3, l: 1}. What is the expected number of occurrences of the pattern 'kl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 2, z: 2, k: 4, e: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'el*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, s: 6, g: 2}. What is the expected number of occurrences of the pattern 'g*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 3, f: 4, n: 5}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, e: 2, s: 3, m: 2, d: 2}. What is the expected number of occurrences of the pattern 'de+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 3, h: 2, r: 3, j: 2, a: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 2, g: 1, m: 2, y: 4, z: 3}, what is the expected number of times the pattern 'a*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 5, e: 4, q: 3} to form a word, what is the expected number of matches of the pattern 'ei+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 2, o: 3, p: 3, q: 4} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 6, v: 2, r: 3, w: 1}, what is the expected number of times the pattern 'xv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.49", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 2, u: 4, q: 3, f: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'c+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, b: 3, r: 3, y: 3}, what is the expected number of times the pattern 'y.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 7, u: 5} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 3, d: 4, p: 5}. What is the expected number of occurrences of the pattern 'd.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 7, b: 2, k: 3}. What is the expected number of occurrences of the pattern 'sb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 4, l: 5, o: 3}. What is the expected number of occurrences of the pattern 'ls*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 1, z: 5, q: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 5, n: 1, r: 4, v: 2}. What is the expected number of occurrences of the pattern 'k.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 2, j: 3, r: 2, b: 5} to form a word, what is the expected number of matches of the pattern 'r*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 2, s: 3, o: 3, e: 4}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 3, j: 9} to form a word, what is the expected number of matches of the pattern 'x.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 2, s: 2, z: 1, q: 3, c: 4}. What is the expected number of occurrences of the pattern 'c*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 5, c: 2, i: 5}, what is the expected number of times the pattern 'i+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.34", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, d: 5, e: 4}, what is the expected number of times the pattern 'e.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 4, w: 2, s: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'ww+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 4, j: 2, t: 1, y: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'h.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 6, d: 6}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 2, q: 4, f: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 5, e: 4, u: 3} to form a word, what is the expected number of matches of the pattern 'eu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 2, v: 4, o: 3, j: 3}. What is the expected number of occurrences of the pattern 'v.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 3, y: 5, f: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 7, x: 5}. What is the expected number of occurrences of the pattern 'nx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 8, q: 4} to form a word, what is the expected number of matches of the pattern 'q*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 5, o: 4, s: 3} to form a word, what is the expected number of matches of the pattern 'os+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 4, o: 1, s: 4, u: 3} to form a word, what is the expected number of matches of the pattern 'o*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 4, i: 6, n: 2} to form a word, what is the expected number of matches of the pattern 'in*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.49", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, s: 1, i: 2, x: 3, y: 2}. What is the expected number of occurrences of the pattern 'i.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 6, y: 6} to form a word, what is the expected number of matches of the pattern 'y.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, i: 8}. What is the expected number of occurrences of the pattern 'l.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 2, i: 6, r: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 5, g: 7} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 1, i: 3, k: 3, m: 5}, what is the expected number of times the pattern 'm+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 2, b: 2, d: 2, h: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'h*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 4, j: 4, k: 4}. What is the expected number of occurrences of the pattern 'x.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 6, u: 4, q: 2}. What is the expected number of occurrences of the pattern 'q.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 5, f: 3, a: 1, i: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'fa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 5, j: 7} to form a word, what is the expected number of matches of the pattern 'j*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 3, u: 3, v: 3, n: 3}. What is the expected number of occurrences of the pattern 'vu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, n: 3, v: 2, j: 2, k: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, i: 7}. What is the expected number of occurrences of the pattern 'i*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 3, e: 3, n: 6}, what is the expected number of times the pattern 'e.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.05", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, q: 4, u: 2, z: 3}, what is the expected number of times the pattern 'u.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 4, i: 5, a: 3}. What is the expected number of occurrences of the pattern 'x*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 3, z: 2, e: 3, u: 3, o: 1} to form a word, what is the expected number of matches of the pattern 'oe+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 1, e: 3, f: 2, q: 4, x: 2}, what is the expected number of times the pattern 'e+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 4, c: 3, j: 5} to form a word, what is the expected number of matches of the pattern 'vc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 6, g: 2, y: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'g.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, l: 2, x: 5, j: 3}. What is the expected number of occurrences of the pattern 'j*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 3, c: 3, h: 5, y: 1}. What is the expected number of occurrences of the pattern 'c+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 6, o: 6}, what is the expected number of times the pattern 'o+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 2, o: 3, j: 3, m: 4} to form a word, what is the expected number of matches of the pattern 'to*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, j: 4, o: 3, i: 2}. What is the expected number of occurrences of the pattern 'oj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 1, m: 5, u: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 7, t: 4, c: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 6, h: 6} to form a word, what is the expected number of matches of the pattern 'dh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 4, u: 3, o: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'u*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 5, i: 7}. What is the expected number of occurrences of the pattern 'io+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, l: 1, e: 3, g: 3, w: 3}. What is the expected number of occurrences of the pattern 'kw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, v: 5, k: 4}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 3, u: 2, d: 3, x: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'du+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 8, o: 4} to form a word, what is the expected number of matches of the pattern 'ao*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 2, q: 3, b: 2, i: 3, l: 2}. What is the expected number of occurrences of the pattern 'q*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 1, s: 4, i: 7} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, k: 5, a: 3}. What is the expected number of occurrences of the pattern 'a.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, h: 4, q: 2, d: 1, m: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 5, o: 2, p: 5} to form a word, what is the expected number of matches of the pattern 'q.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 3, p: 3, n: 6} to form a word, what is the expected number of matches of the pattern 'n+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 5, x: 7}. What is the expected number of occurrences of the pattern 'x*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 4, t: 2, x: 3, b: 1, s: 2}. What is the expected number of occurrences of the pattern 'xs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 8, s: 4}, what is the expected number of times the pattern 's+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 6, b: 6} to form a word, what is the expected number of matches of the pattern 'y*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 8, q: 4}. What is the expected number of occurrences of the pattern 'i+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 6, t: 6}. What is the expected number of occurrences of the pattern 't*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 4, a: 3, l: 1, v: 2, z: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 6, x: 6}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 4, d: 5, l: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 3, t: 2, i: 1, m: 4, d: 2} to form a word, what is the expected number of matches of the pattern 't*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 3, f: 2, u: 2, l: 5}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 2, n: 7, v: 3}, what is the expected number of times the pattern 'zn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 2, y: 5, g: 3, a: 2}. What is the expected number of occurrences of the pattern 'ya*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 2, p: 5, a: 5}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 4, a: 4, t: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'td*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 7, o: 5} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 2, x: 5, r: 5} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 3, c: 3, e: 3, s: 3}. What is the expected number of occurrences of the pattern 'ce+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 7, b: 1, f: 3, y: 1}, what is the expected number of times the pattern 'f.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 3, o: 2, c: 3, w: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'd+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 5, c: 7}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 3, t: 3, u: 3, k: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'u.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {u: 5, x: 7} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 4, z: 6, i: 2}. What is the expected number of occurrences of the pattern 'z.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, k: 2, m: 4, o: 2}, what is the expected number of times the pattern 'k+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, q: 2, t: 5, o: 2}, what is the expected number of times the pattern 't*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 2, p: 3, l: 2, r: 3, n: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 5, h: 7} to form a word, what is the expected number of matches of the pattern 'h+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 2, p: 2, j: 6, o: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'o+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 2, b: 3, d: 7}, what is the expected number of times the pattern 't*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 3, i: 2, n: 3, p: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'vi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 2, u: 1, p: 3, w: 2, j: 4}. What is the expected number of occurrences of the pattern 'p.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, g: 8}. What is the expected number of occurrences of the pattern 'g+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 1, g: 2, e: 3, i: 2, r: 4}. What is the expected number of occurrences of the pattern 'gn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 4, w: 8}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 8, l: 4} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, r: 3, l: 2, g: 3, c: 1}, what is the expected number of times the pattern 'g+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 7, c: 5} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 3, c: 3, u: 2, k: 4}. What is the expected number of occurrences of the pattern 'k+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 3, x: 3, v: 6} to form a word, what is the expected number of matches of the pattern 'v.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 5, t: 7}. What is the expected number of occurrences of the pattern 'u.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 1, p: 3, s: 3, f: 5}. What is the expected number of occurrences of the pattern 'f+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, q: 6, k: 3}, what is the expected number of times the pattern 'v*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, j: 5, m: 4}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 2, v: 1, t: 6, r: 3}. What is the expected number of occurrences of the pattern 'vr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 3, r: 3, z: 4, t: 2}. What is the expected number of occurrences of the pattern 't.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, z: 3, r: 4, o: 2}, what is the expected number of times the pattern 'v+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 6, w: 6}. What is the expected number of occurrences of the pattern 'l.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 4, n: 2, w: 4, b: 2}. What is the expected number of occurrences of the pattern 'n*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 1, y: 4, b: 2, t: 2, m: 3} to form a word, what is the expected number of matches of the pattern 't*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 4, e: 3, n: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, t: 4, l: 5}, what is the expected number of times the pattern 'lt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 3, b: 9} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 4, n: 3, j: 5}. What is the expected number of occurrences of the pattern 'nj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 4, h: 1, b: 2, l: 5} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, n: 4, p: 1, r: 2, i: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 6, q: 3, z: 3}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 8, u: 4}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 3, h: 3, k: 3, l: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 4, q: 2, u: 4, o: 2}, what is the expected number of times the pattern 'k.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 5, i: 4, e: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 2, a: 4, t: 3, o: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'w*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 4, n: 3, q: 5}. What is the expected number of occurrences of the pattern 'nq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 4, n: 3, v: 5} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 1, y: 3, o: 4, k: 3, e: 1}, what is the expected number of times the pattern 'ye*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 5, g: 4, n: 1, a: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, o: 2, k: 2, t: 2, q: 3}, what is the expected number of times the pattern 'o+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, d: 3, y: 4, g: 2}, what is the expected number of times the pattern 'd.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 3, k: 5, c: 4}, what is the expected number of times the pattern 'k+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, u: 4, g: 3, s: 2}, what is the expected number of times the pattern 'g+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 3, o: 2, c: 5, b: 2}, what is the expected number of times the pattern 'cc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 5, o: 1, i: 3, y: 3}, what is the expected number of times the pattern 'iy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 7, c: 5} to form a word, what is the expected number of matches of the pattern 'dc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, m: 4, f: 1, w: 2, i: 3}. What is the expected number of occurrences of the pattern 'm.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 2, a: 4, e: 4, x: 2}. What is the expected number of occurrences of the pattern 'e*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 5, j: 2, i: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, p: 3, s: 3, h: 3}. What is the expected number of occurrences of the pattern 'pk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 4, u: 4, a: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 5, d: 3, n: 4}. What is the expected number of occurrences of the pattern 'nd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 5, z: 3, p: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'nz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, t: 4, a: 1, h: 2, f: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 4, p: 1, i: 7}, what is the expected number of times the pattern 'ph+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 5, a: 7}, what is the expected number of times the pattern 'la*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 6, j: 6} to form a word, what is the expected number of matches of the pattern 'jo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 4, t: 4, c: 4}, what is the expected number of times the pattern 'c*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 4, u: 3, i: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'i*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 4, j: 2, z: 2, h: 4}, what is the expected number of times the pattern 'z*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 2, p: 3, m: 2, r: 2, a: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 6, i: 6}. What is the expected number of occurrences of the pattern 'li+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, n: 4, y: 1, e: 2, l: 2}, what is the expected number of times the pattern 'n+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 6, b: 6}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 1, k: 6, u: 1, b: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 3, s: 4, k: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 6, d: 3, y: 3}. What is the expected number of occurrences of the pattern 'y+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 5, c: 1, f: 1, o: 5}, what is the expected number of times the pattern 'o+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.34", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 3, f: 2, r: 4, n: 3} to form a word, what is the expected number of matches of the pattern 'e.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 5, y: 7} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 1, j: 7, u: 3, l: 1}, what is the expected number of times the pattern 'aj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 5, c: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'c+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 3, q: 3, w: 2, c: 2, i: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 5, o: 7}, what is the expected number of times the pattern 'o*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 6, i: 6}. What is the expected number of occurrences of the pattern 'i*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 2, t: 5, x: 2, h: 3} to form a word, what is the expected number of matches of the pattern 't+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.54", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, t: 3, r: 4, s: 1, h: 1}, what is the expected number of times the pattern 're*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 3, d: 4, j: 4, v: 1}. What is the expected number of occurrences of the pattern 'u*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 5, z: 7} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, u: 5, p: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, d: 3, y: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 2, b: 6, z: 4} to form a word, what is the expected number of matches of the pattern 'zz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 5, s: 3, d: 4}. What is the expected number of occurrences of the pattern 'sp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 3, j: 4, n: 2, h: 3}. What is the expected number of occurrences of the pattern 'n+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 3, k: 6, g: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 8, b: 4}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 3, q: 3, m: 4, u: 2}. What is the expected number of occurrences of the pattern 'u+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 2, e: 3, u: 4, n: 1, v: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 7, i: 5}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 4, z: 2, a: 6}, what is the expected number of times the pattern 'zn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, r: 4, a: 3, q: 2}, what is the expected number of times the pattern 'r*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 3, o: 2, d: 1, x: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'x+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 7, j: 1, g: 4}. What is the expected number of occurrences of the pattern 'e.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 3, h: 3, z: 4, o: 2}. What is the expected number of occurrences of the pattern 'oh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 1, y: 7, d: 4}. What is the expected number of occurrences of the pattern 'y+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 2, f: 2, b: 2, i: 6} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 7, b: 5} to form a word, what is the expected number of matches of the pattern 'mm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 5, x: 2, h: 3, p: 2}. What is the expected number of occurrences of the pattern 'hx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, u: 3, e: 1, a: 5}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 2, s: 3, c: 1, z: 6}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 3, w: 2, j: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 7, q: 1, m: 1, k: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 2, z: 3, i: 5, m: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 1, d: 4, m: 2, n: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'd+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 4, y: 3, k: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'y+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 6, c: 6}. What is the expected number of occurrences of the pattern 'ck*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 7, z: 5}, what is the expected number of times the pattern 'z+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 6, f: 3, s: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 5, h: 3, z: 4}. What is the expected number of occurrences of the pattern 'cz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 4, c: 8} to form a word, what is the expected number of matches of the pattern 'cw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 2, d: 2, m: 4, r: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'mo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 6, a: 3, p: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 1, j: 2, s: 2, i: 3, l: 4} to form a word, what is the expected number of matches of the pattern 's*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 1, n: 4, z: 5, i: 2}. What is the expected number of occurrences of the pattern 'w.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {u: 3, h: 5, o: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 3, d: 9}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 1, n: 4, o: 7} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 6, s: 3, h: 3}. What is the expected number of occurrences of the pattern 'h*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 5, w: 1, f: 1, g: 2, n: 3}. What is the expected number of occurrences of the pattern 'w+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 7, k: 5}, what is the expected number of times the pattern 'f*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 3, f: 6, q: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, v: 5, p: 2, e: 2}, what is the expected number of times the pattern 'vn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 3, c: 2, v: 4, z: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 3, f: 2, s: 3, a: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'f.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 1, a: 2, f: 3, g: 5, z: 1}, what is the expected number of times the pattern 'ah+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 3, u: 3, s: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'vs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 5, x: 1, j: 1, m: 5} to form a word, what is the expected number of matches of the pattern 'xm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 4, k: 2, w: 6}. What is the expected number of occurrences of the pattern 'qw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 2, h: 2, e: 1, u: 5, b: 2} to form a word, what is the expected number of matches of the pattern 'e*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 2, j: 4, v: 3, c: 3}, what is the expected number of times the pattern 'n+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 6, g: 6}. What is the expected number of occurrences of the pattern 'z*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 5, k: 5, d: 2} to form a word, what is the expected number of matches of the pattern 'j+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.34", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 5, d: 5, p: 2}, what is the expected number of times the pattern 'dm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.34", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 8, b: 4}. What is the expected number of occurrences of the pattern 'ii*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.74", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 6, m: 6} to form a word, what is the expected number of matches of the pattern 'mb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 3, m: 5, g: 4} to form a word, what is the expected number of matches of the pattern 'tm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 2, s: 7, b: 3} to form a word, what is the expected number of matches of the pattern 's*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 4, i: 8}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 3, b: 3, u: 3, l: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 4, v: 8} to form a word, what is the expected number of matches of the pattern 'g*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 4, g: 2, j: 2, o: 4}, what is the expected number of times the pattern 'o+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, m: 4, x: 1, y: 2, c: 1}, what is the expected number of times the pattern 'cy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 6, e: 6}. What is the expected number of occurrences of the pattern 't*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 2, x: 2, z: 3, r: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, a: 7}. What is the expected number of occurrences of the pattern 'a.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, d: 2, l: 3, c: 5}. What is the expected number of occurrences of the pattern 'ld+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 7, h: 5}. What is the expected number of occurrences of the pattern 'h.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 2, d: 7, t: 3} to form a word, what is the expected number of matches of the pattern 't*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 3, f: 2, y: 2, w: 4, v: 1}, what is the expected number of times the pattern 'ft+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 2, o: 2, y: 2, m: 4, v: 2}, what is the expected number of times the pattern 'v*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 3, d: 3, y: 3, q: 2, e: 1}. What is the expected number of occurrences of the pattern 'j+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 2, m: 4, q: 2, z: 4}. What is the expected number of occurrences of the pattern 'm+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 5, e: 7}. What is the expected number of occurrences of the pattern 'ep*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 4, w: 2, y: 1, j: 2, p: 3}, what is the expected number of times the pattern 'p+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 3, d: 5, y: 4}. What is the expected number of occurrences of the pattern 'y+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 2, p: 3, n: 4, w: 1, s: 2}. What is the expected number of occurrences of the pattern 'l+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 7, b: 5}, what is the expected number of times the pattern 'o+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 3, k: 4, r: 5}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, x: 5, j: 3, y: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 4, g: 4, w: 4} to form a word, what is the expected number of matches of the pattern 'gw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 3, a: 2, n: 2, v: 3, q: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 4, d: 4, p: 4}, what is the expected number of times the pattern 'wp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 1, u: 3, p: 2, x: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 4, d: 3, h: 4, b: 1} to form a word, what is the expected number of matches of the pattern 'a.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 5, f: 7}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 3, h: 2, z: 3, y: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'y+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 2, h: 2, r: 2, d: 2, v: 4}. What is the expected number of occurrences of the pattern 'd*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, q: 4, u: 5}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 1, h: 2, g: 4, w: 3, d: 2}, what is the expected number of times the pattern 'g+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 2, s: 2, b: 3, r: 5}. What is the expected number of occurrences of the pattern 'l.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 1, p: 3, u: 3, a: 3, i: 2}, what is the expected number of times the pattern 'pa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 6, t: 2, v: 2, a: 2}, what is the expected number of times the pattern 'vd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 2, y: 2, e: 2, a: 2, m: 4}, what is the expected number of times the pattern 'ye+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 1, u: 5, f: 3, l: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'lo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 2, m: 4, r: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'r+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 4, q: 3, j: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'oj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 3, n: 1, y: 3, k: 3, h: 2}. What is the expected number of occurrences of the pattern 'k+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, m: 2, y: 3, a: 2, j: 2}, what is the expected number of times the pattern 'm+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 3, t: 4, f: 2, p: 2, o: 1}. What is the expected number of occurrences of the pattern 'oy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 6, x: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 8, z: 4}, what is the expected number of times the pattern 'gz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 1, s: 2, r: 6, k: 1, v: 2}. What is the expected number of occurrences of the pattern 'p+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 4, k: 3, n: 5}. What is the expected number of occurrences of the pattern 'o*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 4, h: 8} to form a word, what is the expected number of matches of the pattern 'oh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 4, h: 3, s: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'h.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, q: 4, k: 2, z: 3}, what is the expected number of times the pattern 'z+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 2, s: 4, b: 1, g: 4, t: 1}, what is the expected number of times the pattern 'e.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, y: 4, t: 5}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 8, h: 4} to form a word, what is the expected number of matches of the pattern 'a+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 2, a: 1, d: 3, m: 5, w: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 6, a: 6}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 6, b: 6}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 4, s: 7, m: 1} to form a word, what is the expected number of matches of the pattern 's+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 4, f: 3, l: 1, j: 2, e: 2}, what is the expected number of times the pattern 'f.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 4, l: 4, p: 4}. What is the expected number of occurrences of the pattern 'l*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, g: 3, l: 2, c: 4}, what is the expected number of times the pattern 'g*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 5, k: 5, i: 2}. What is the expected number of occurrences of the pattern 'ik+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.54", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 7, f: 5}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, n: 3, a: 3, e: 3}, what is the expected number of times the pattern 'ra+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {u: 5, c: 7} to form a word, what is the expected number of matches of the pattern 'cu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 3, v: 1, i: 5, x: 3} to form a word, what is the expected number of matches of the pattern 'v*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, r: 8}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 4, h: 1, c: 3, p: 1, l: 3}. What is the expected number of occurrences of the pattern 'hp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 4, o: 8}, what is the expected number of times the pattern 'a+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, r: 5, s: 1, q: 2, g: 2}. What is the expected number of occurrences of the pattern 'r.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, o: 3, q: 2, k: 3, c: 1}. What is the expected number of occurrences of the pattern 'q.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 6, d: 6} to form a word, what is the expected number of matches of the pattern 'dw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 1, g: 6, w: 5}. What is the expected number of occurrences of the pattern 'g+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 3, p: 3, b: 4, i: 2}. What is the expected number of occurrences of the pattern 'jp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 2, v: 1, l: 4, z: 5}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 4, d: 3, z: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, c: 4, a: 3}. What is the expected number of occurrences of the pattern 'cs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 5, g: 5, o: 2}, what is the expected number of times the pattern 'o*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 1, o: 2, n: 4, z: 5} to form a word, what is the expected number of matches of the pattern 'n+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 4, q: 5, w: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 6, q: 6}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 6, z: 1, u: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'dl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 7, u: 5} to form a word, what is the expected number of matches of the pattern 'u*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 4, e: 2, n: 6}. What is the expected number of occurrences of the pattern 'n.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, i: 9}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 3, h: 3, x: 4, e: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, v: 3, l: 2, u: 2, y: 3}. What is the expected number of occurrences of the pattern 'u.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 5, y: 7}. What is the expected number of occurrences of the pattern 'py*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 6, h: 6}, what is the expected number of times the pattern 'ph*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 6, s: 6}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 7, n: 5}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 1, f: 1, y: 1, m: 7, d: 2} to form a word, what is the expected number of matches of the pattern 'fy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 3, q: 4, t: 5}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 4, h: 1, u: 1, s: 4, v: 2}, what is the expected number of times the pattern 'jv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 3, x: 3, u: 3, n: 1, t: 2}. What is the expected number of occurrences of the pattern 'nb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 9, c: 3}, what is the expected number of times the pattern 'cx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 5, d: 1, t: 6}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 7, u: 5}. What is the expected number of occurrences of the pattern 'u*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, g: 3, z: 5}, what is the expected number of times the pattern 'gp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 1, y: 4, l: 3, g: 2, d: 2}. What is the expected number of occurrences of the pattern 'gd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 5, o: 7}. What is the expected number of occurrences of the pattern 'wo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 6, d: 4, k: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 3, r: 5, b: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 3, a: 1, q: 6, o: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 2, h: 5, i: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 3, u: 3, z: 6}. What is the expected number of occurrences of the pattern 'z+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 2, x: 1, p: 4, j: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'cm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 4, v: 2, l: 3, r: 3}. What is the expected number of occurrences of the pattern 'lr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 1, x: 4, p: 3, b: 3, q: 1}. What is the expected number of occurrences of the pattern 'ss*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 5, l: 7}. What is the expected number of occurrences of the pattern 'i.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 3, m: 4, r: 5}. What is the expected number of occurrences of the pattern 'r+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 4, o: 3, y: 5} to form a word, what is the expected number of matches of the pattern 'ow+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 5, u: 4, z: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 3, m: 5, q: 4}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 8, x: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 3, q: 4, b: 2, d: 1, f: 2}. What is the expected number of occurrences of the pattern 'f+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 5, v: 7}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 2, e: 2, h: 3, a: 4, d: 1}, what is the expected number of times the pattern 'a.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 7, q: 5}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 2, n: 6, m: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'zx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 5, p: 1, e: 6}, what is the expected number of times the pattern 'p*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.69", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 3, m: 4, f: 1, o: 4} to form a word, what is the expected number of matches of the pattern 'of*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, g: 2, w: 3, m: 2, v: 2}. What is the expected number of occurrences of the pattern 'm.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 2, i: 2, a: 4, d: 2, f: 2}. What is the expected number of occurrences of the pattern 'di*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 1, u: 2, r: 5, p: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'ku+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 3, s: 2, u: 1, m: 3, o: 3}, what is the expected number of times the pattern 's.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, k: 1, f: 2, a: 5}. What is the expected number of occurrences of the pattern 'f*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 1, z: 4, x: 3, n: 4}. What is the expected number of occurrences of the pattern 'x*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, g: 3, s: 5, i: 1}, what is the expected number of times the pattern 'is+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 2, x: 2, f: 1, e: 3, z: 4}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 1, y: 3, q: 1, o: 3, m: 4}. What is the expected number of occurrences of the pattern 'q+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 7, r: 5} to form a word, what is the expected number of matches of the pattern 'o+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, x: 6, v: 4}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, o: 8}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 2, f: 4, s: 3, h: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, q: 3, o: 5}. What is the expected number of occurrences of the pattern 'no+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 4, x: 3, p: 5} to form a word, what is the expected number of matches of the pattern 'x.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 2, n: 5, i: 3, f: 1, b: 1}, what is the expected number of times the pattern 'i.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 1, n: 2, h: 3, a: 6} to form a word, what is the expected number of matches of the pattern 'am*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 3, r: 4, j: 2, i: 2, k: 1}. What is the expected number of occurrences of the pattern 'ij*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 6, q: 6} to form a word, what is the expected number of matches of the pattern 'q*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 4, u: 1, y: 5, s: 2}, what is the expected number of times the pattern 'd+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 2, c: 2, f: 3, m: 3, s: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 3, s: 3, o: 6} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 2, l: 5, p: 5} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 1, c: 6, u: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 3, f: 5, y: 4} to form a word, what is the expected number of matches of the pattern 'fy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 3, l: 5, b: 4} to form a word, what is the expected number of matches of the pattern 'll+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 7, b: 5}. What is the expected number of occurrences of the pattern 'u*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 7, g: 5}. What is the expected number of occurrences of the pattern 'm+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 1, h: 2, d: 1, j: 4, y: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 2, y: 1, r: 3, s: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'y+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, n: 4, l: 4}, what is the expected number of times the pattern 'l.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 3, m: 2, q: 2, z: 3, e: 2}, what is the expected number of times the pattern 'k.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 2, i: 2, v: 5, n: 3} to form a word, what is the expected number of matches of the pattern 'i*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 2, j: 7, b: 3} to form a word, what is the expected number of matches of the pattern 'nj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 5, q: 4, e: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 3, a: 4, s: 1, g: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'qg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 3, m: 3, f: 6} to form a word, what is the expected number of matches of the pattern 'n+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 4, k: 8}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 4, c: 2, l: 3, d: 1, g: 2}. What is the expected number of occurrences of the pattern 'g+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, h: 7, d: 1}, what is the expected number of times the pattern 'dh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.47", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {u: 3, z: 4, d: 1, o: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'u.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, y: 4, a: 2, z: 3}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 3, i: 4, l: 3, p: 2}. What is the expected number of occurrences of the pattern 'i*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {u: 2, k: 2, n: 2, d: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'k+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 3, d: 2, o: 3, e: 2, y: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 8, q: 4}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 9, m: 3}. What is the expected number of occurrences of the pattern 'c*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 1, h: 1, m: 5, w: 2, x: 3}, what is the expected number of times the pattern 'k+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 1, u: 4, j: 5, t: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 1, b: 3, i: 3, w: 3, u: 2}, what is the expected number of times the pattern 'w.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 1, q: 3, y: 3, r: 5} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 9, n: 3} to form a word, what is the expected number of matches of the pattern 'n.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 5, d: 1, b: 2, i: 3, a: 1}. What is the expected number of occurrences of the pattern 'd*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 3, w: 2, u: 2, b: 3, y: 2} to form a word, what is the expected number of matches of the pattern 'u+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 4, f: 5, r: 3}, what is the expected number of times the pattern 'r.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 5, u: 7}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 5, z: 1, e: 1, o: 2, v: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, q: 3, d: 3, m: 1, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 6, r: 6}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 5, g: 5, r: 2}. What is the expected number of occurrences of the pattern 'g.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 2, x: 3, q: 2, c: 5}. What is the expected number of occurrences of the pattern 'q.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 5, q: 7} to form a word, what is the expected number of matches of the pattern 'q*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 4, y: 2, d: 4, v: 2}. What is the expected number of occurrences of the pattern 'y*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 1, o: 4, x: 4, u: 3}, what is the expected number of times the pattern 'uo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 5, p: 3, w: 4}, what is the expected number of times the pattern 'z*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, s: 1, p: 2, w: 2, g: 4}, what is the expected number of times the pattern 'w+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 1, f: 4, g: 2, l: 3, p: 2}. What is the expected number of occurrences of the pattern 'p*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 4, x: 3, s: 2, n: 3}, what is the expected number of times the pattern 'xn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 4, x: 8}. What is the expected number of occurrences of the pattern 'x+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 6, i: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'nt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.49", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 4, g: 3, e: 5}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 3, o: 3, h: 1, g: 2, z: 3}. What is the expected number of occurrences of the pattern 'w+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 3, i: 2, s: 2, q: 3, r: 2}, what is the expected number of times the pattern 'i*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 8, n: 4} to form a word, what is the expected number of matches of the pattern 'g*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 5, m: 7}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 4, i: 4, y: 4}. What is the expected number of occurrences of the pattern 'i+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 2, s: 3, m: 5, n: 2} to form a word, what is the expected number of matches of the pattern 'j*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 4, a: 3, u: 5}. What is the expected number of occurrences of the pattern 'au*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 3, n: 3, o: 6}, what is the expected number of times the pattern 'p+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 4, e: 4, y: 4}. What is the expected number of occurrences of the pattern 'ye+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 6, x: 6}. What is the expected number of occurrences of the pattern 'yx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 2, g: 3, p: 2, q: 3, o: 2}. What is the expected number of occurrences of the pattern 'p.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 3, f: 3, s: 2, b: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'c+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 4, n: 2, k: 2, s: 4}, what is the expected number of times the pattern 'sn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 2, j: 2, l: 4, o: 1, p: 3}, what is the expected number of times the pattern 'w.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 7, w: 5} to form a word, what is the expected number of matches of the pattern 'dw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 5, m: 3, t: 2, f: 1, x: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 5, l: 7}. What is the expected number of occurrences of the pattern 'l.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 4, m: 1, g: 2, q: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'p.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 8, n: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 2, j: 3, f: 7} to form a word, what is the expected number of matches of the pattern 'j.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 4, z: 8} to form a word, what is the expected number of matches of the pattern 'z*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.74", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 7, k: 2, y: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 7, g: 5}. What is the expected number of occurrences of the pattern 'g.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 5, h: 2, b: 5}. What is the expected number of occurrences of the pattern 'cc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 1, i: 4, f: 3, t: 4}, what is the expected number of times the pattern 'i*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, i: 3, g: 4, r: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, h: 2, c: 2, g: 5}. What is the expected number of occurrences of the pattern 'k.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, t: 3, h: 5, g: 2}. What is the expected number of occurrences of the pattern 'h+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.54", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 3, r: 3, o: 1, d: 5}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 4, q: 8}, what is the expected number of times the pattern 'qs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 3, c: 3, g: 4, k: 2}. What is the expected number of occurrences of the pattern 'ce*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 3, z: 1, d: 2, c: 6}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 2, y: 4, c: 6}. What is the expected number of occurrences of the pattern 'y+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 3, x: 2, w: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'w+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 1, b: 3, r: 3, c: 1, p: 4}, what is the expected number of times the pattern 'kp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, o: 9}, what is the expected number of times the pattern 'o.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 7, n: 5}. What is the expected number of occurrences of the pattern 'un*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 8, x: 4} to form a word, what is the expected number of matches of the pattern 'w.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 5, x: 4, s: 1, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 4, l: 5, w: 3}, what is the expected number of times the pattern 'l+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 7, b: 5} to form a word, what is the expected number of matches of the pattern 'm*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 6, a: 6}, what is the expected number of times the pattern 'z+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 2, n: 2, a: 3, c: 2, g: 3}. What is the expected number of occurrences of the pattern 'n.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 2, s: 3, c: 3, l: 4}. What is the expected number of occurrences of the pattern 'l+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 5, y: 2, p: 4, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 5, i: 7}, what is the expected number of times the pattern 'm+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 2, m: 2, d: 3, w: 5}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 6, f: 6} to form a word, what is the expected number of matches of the pattern 's.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 6, x: 2, h: 4}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 2, m: 5, d: 2, a: 1, x: 2}. What is the expected number of occurrences of the pattern 'ax+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 4, j: 4, w: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'v.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 5, g: 3, w: 2, d: 2}. What is the expected number of occurrences of the pattern 'w*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, q: 2, a: 2, n: 2, c: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 4, q: 8} to form a word, what is the expected number of matches of the pattern 'z.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 4, y: 8}, what is the expected number of times the pattern 'y+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 1, y: 2, o: 5, t: 3, a: 1}, what is the expected number of times the pattern 'y+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 5, b: 7} to form a word, what is the expected number of matches of the pattern 'l+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 6, l: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'l.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 2, w: 2, j: 3, q: 5}. What is the expected number of occurrences of the pattern 'tw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 7, c: 5} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 5, h: 2, p: 1, k: 4}, what is the expected number of times the pattern 'h*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 5, t: 7}, what is the expected number of times the pattern 't+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 5, e: 7} to form a word, what is the expected number of matches of the pattern 'oe+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 11, c: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 4, e: 8} to form a word, what is the expected number of matches of the pattern 'ie*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 1, d: 11}. What is the expected number of occurrences of the pattern 's.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 2, z: 3, o: 5, p: 2}, what is the expected number of times the pattern 'pz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 2, i: 2, h: 2, o: 3, g: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 3, n: 7, p: 2}, what is the expected number of times the pattern 'n+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 1, u: 1, h: 3, s: 3, q: 4} to form a word, what is the expected number of matches of the pattern 'u+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 9, m: 3}, what is the expected number of times the pattern 'm*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, u: 4, i: 3, r: 2}, what is the expected number of times the pattern 'u*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 8, i: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 4, n: 4, c: 4}, what is the expected number of times the pattern 'c.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, h: 3, l: 5}. What is the expected number of occurrences of the pattern 'hi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 7, k: 5} to form a word, what is the expected number of matches of the pattern 'kd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 4, q: 3, g: 5}. What is the expected number of occurrences of the pattern 'qo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 1, h: 1, z: 2, g: 3, k: 5}, what is the expected number of times the pattern 'j*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, g: 5, o: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, m: 3, e: 2, q: 2, w: 2}, what is the expected number of times the pattern 'mw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 4, b: 2, x: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, d: 3, t: 6}. What is the expected number of occurrences of the pattern 't*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 5, d: 5, l: 2}, what is the expected number of times the pattern 'h.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 5, z: 3, g: 2, r: 2}. What is the expected number of occurrences of the pattern 'r*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 7, k: 2, o: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 7, o: 5}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, p: 3, a: 6}, what is the expected number of times the pattern 'a.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.05", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 3, t: 1, x: 2, b: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'xt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 5, f: 4, i: 3}. What is the expected number of occurrences of the pattern 'f+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 5, i: 7}, what is the expected number of times the pattern 'd*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {a: 5, y: 2, u: 1, t: 2, i: 2}. What is the expected number of occurrences of the pattern 'y.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 6, e: 6} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 7, u: 5}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 3, v: 4, i: 1, p: 2, l: 2}. What is the expected number of occurrences of the pattern 'ie+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 2, r: 3, h: 1, d: 4, j: 2}. What is the expected number of occurrences of the pattern 'rd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {u: 5, g: 2, z: 5} to form a word, what is the expected number of matches of the pattern 'g*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 5, v: 7} to form a word, what is the expected number of matches of the pattern 'm.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 3, i: 2, l: 3, x: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'l.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 4, z: 2, f: 3, y: 1, x: 2}. What is the expected number of occurrences of the pattern 'dx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 3, b: 2, l: 4, z: 3} to form a word, what is the expected number of matches of the pattern 'zz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 1, r: 2, j: 4, z: 5}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 6, j: 6}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, f: 5, m: 2, r: 2, y: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 4, w: 2, y: 4, b: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 4, h: 2, i: 1, q: 5}. What is the expected number of occurrences of the pattern 'q*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, b: 4, l: 2, h: 1, y: 2}, what is the expected number of times the pattern 'h+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 7, u: 5} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 6, t: 6}. What is the expected number of occurrences of the pattern 'o*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {e: 6, g: 6}. What is the expected number of occurrences of the pattern 'e+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, q: 1, f: 4, n: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 2, j: 3, m: 3, c: 4}, what is the expected number of times the pattern 'mc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 3, e: 4, a: 5} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 6, o: 6}. What is the expected number of occurrences of the pattern 'd*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 4, v: 3, z: 2, f: 3}, what is the expected number of times the pattern 'f*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 4, t: 2, m: 6}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, y: 4, z: 1, v: 3, s: 1}, what is the expected number of times the pattern 'y.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 2, g: 10}, what is the expected number of times the pattern 'og+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 6, s: 4, e: 2} to form a word, what is the expected number of matches of the pattern 's+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 3, o: 3, l: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 6, h: 6}. What is the expected number of occurrences of the pattern 'hf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 4, p: 4, x: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, d: 3, w: 2, f: 2, r: 2}, what is the expected number of times the pattern 'fw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, r: 2, y: 4, o: 3}, what is the expected number of times the pattern 'o+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 4, a: 1, f: 7}. What is the expected number of occurrences of the pattern 'a.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 5, s: 2, t: 5} to form a word, what is the expected number of matches of the pattern 't.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 5, l: 3, a: 2, w: 2}. What is the expected number of occurrences of the pattern 'a*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 4, o: 8}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 3, k: 5, o: 4}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {z: 5, j: 7}. What is the expected number of occurrences of the pattern 'jz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, k: 8}. What is the expected number of occurrences of the pattern 'nk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, l: 3, u: 4, k: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 3, h: 4, n: 3, z: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 3, s: 1, k: 4, n: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'n*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, w: 3, j: 3, s: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 3, z: 2, y: 1, h: 5, u: 1} to form a word, what is the expected number of matches of the pattern 'zj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 3, a: 5, p: 4}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 7, v: 5}, what is the expected number of times the pattern 'vp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 3, r: 2, h: 3, e: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 3, i: 2, k: 3, d: 4} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, i: 1, r: 2, w: 5, t: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, z: 5, d: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 4, l: 8}, what is the expected number of times the pattern 'l+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 4, m: 1, q: 5, v: 2} to form a word, what is the expected number of matches of the pattern 'iv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {v: 2, k: 3, f: 1, c: 4, x: 2}. What is the expected number of occurrences of the pattern 'f+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 6, f: 3, y: 3}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 3, b: 3, l: 6}, what is the expected number of times the pattern 'u+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {w: 8, m: 4}. What is the expected number of occurrences of the pattern 'mw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 4, k: 5, v: 3}, what is the expected number of times the pattern 'k+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 5, l: 7}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, p: 8, j: 2}. What is the expected number of occurrences of the pattern 'p.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 3, k: 1, m: 4, v: 2, t: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 2, g: 1, l: 4, z: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'zl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 3, u: 4, b: 2, e: 3}. What is the expected number of occurrences of the pattern 'u+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 1, c: 4, p: 3, y: 4} to form a word, what is the expected number of matches of the pattern 'cp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 2, f: 2, z: 3, m: 1, a: 4} to form a word, what is the expected number of matches of the pattern 'zq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 3, c: 4, h: 3, z: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'h*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 4, o: 2, t: 1, f: 5} to form a word, what is the expected number of matches of the pattern 'or+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, b: 4, l: 5}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 3, y: 1, k: 4, c: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 6, w: 6} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 2, w: 6, s: 2, i: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 4, s: 3, w: 2, m: 3}, what is the expected number of times the pattern 'm.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 4, c: 8}. What is the expected number of occurrences of the pattern 'mc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 2, w: 3, e: 4, d: 1, v: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 3, n: 2, e: 3, b: 4} to form a word, what is the expected number of matches of the pattern 'e*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 2, r: 4, s: 2, b: 1, c: 3}, what is the expected number of times the pattern 'rs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, j: 5, k: 4}, what is the expected number of times the pattern 'kj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 3, t: 3, p: 2, e: 1, z: 3}. What is the expected number of occurrences of the pattern 'zt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {v: 4, h: 4, j: 3, s: 1} to form a word, what is the expected number of matches of the pattern 's*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 5, y: 5, l: 2} to form a word, what is the expected number of matches of the pattern 'a*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.84", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 6, y: 6} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, h: 5, c: 5}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 3, y: 3, z: 6}, what is the expected number of times the pattern 'zy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 3, x: 4, r: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'p+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 4, w: 4, f: 4}, what is the expected number of times the pattern 'f*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 4, f: 1, w: 3, l: 4}, what is the expected number of times the pattern 'l.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 1, x: 2, p: 4, l: 5}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 6, n: 6}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, c: 7}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, m: 5, z: 4}. What is the expected number of occurrences of the pattern 'z+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 3, g: 3, a: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'ug*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, p: 3, z: 5}. What is the expected number of occurrences of the pattern 'p.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, j: 2, m: 4, y: 3}. What is the expected number of occurrences of the pattern 'y.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 3, o: 3, b: 1, l: 5} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 1, n: 5, c: 4, q: 2}. What is the expected number of occurrences of the pattern 'q+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 4, l: 3, x: 5} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 5, x: 4, v: 3}, what is the expected number of times the pattern 'x.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 4, l: 8}, what is the expected number of times the pattern 'l.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {h: 3, a: 3, g: 1, v: 5} to form a word, what is the expected number of matches of the pattern 'v*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 1, l: 3, w: 4, t: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {y: 4, t: 2, m: 3, f: 2, u: 1}. What is the expected number of occurrences of the pattern 'my*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 2, x: 3, s: 3, u: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'u.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 4, x: 5, r: 3}. What is the expected number of occurrences of the pattern 'x+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 6, r: 1, x: 5} to form a word, what is the expected number of matches of the pattern 'rx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 1, z: 2, a: 6, o: 1, u: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 1, m: 2, y: 5, d: 2, c: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 7, o: 5}, what is the expected number of times the pattern 'g.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 2, n: 2, f: 3, q: 2, t: 3}, what is the expected number of times the pattern 'q.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 2, w: 2, x: 3, q: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 2, n: 5, z: 3, k: 1, t: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 6, q: 2, v: 3, x: 1}. What is the expected number of occurrences of the pattern 'q.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 6, b: 2, g: 1, i: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'w.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 3, t: 4, o: 5} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 3, w: 5, o: 4} to form a word, what is the expected number of matches of the pattern 'o.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 6, y: 5, e: 1} to form a word, what is the expected number of matches of the pattern 'x.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 4, s: 8}. What is the expected number of occurrences of the pattern 'j.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 3, n: 2, d: 3, e: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 3, t: 6, e: 3} to form a word, what is the expected number of matches of the pattern 'xt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, a: 8}, what is the expected number of times the pattern 'p+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 1, i: 3, y: 4, q: 2, e: 2}, what is the expected number of times the pattern 'q*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 1, t: 2, z: 3, f: 5, s: 1} to form a word, what is the expected number of matches of the pattern 'z.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 5, c: 4, x: 3}. What is the expected number of occurrences of the pattern 'tx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 7, n: 5}, what is the expected number of times the pattern 'dn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, o: 8}. What is the expected number of occurrences of the pattern 't.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {c: 3, o: 2, g: 1, q: 3, k: 3}. What is the expected number of occurrences of the pattern 'ok*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 2, i: 2, j: 4, e: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 4, p: 8} to form a word, what is the expected number of matches of the pattern 's+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 4, u: 3, q: 5}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 6, s: 6}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 4, x: 2, s: 6} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 7, m: 5}, what is the expected number of times the pattern 'qm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 2, q: 3, l: 1, c: 6}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 2, o: 3, t: 5, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 5, g: 7} to form a word, what is the expected number of matches of the pattern 'ig*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, v: 3, t: 1, r: 2, p: 4}. What is the expected number of occurrences of the pattern 't+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 6, j: 6}, what is the expected number of times the pattern 'j.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {i: 7, w: 5} to form a word, what is the expected number of matches of the pattern 'w*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {r: 2, k: 1, x: 3, u: 2, h: 4}. What is the expected number of occurrences of the pattern 'h+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 5, l: 1, p: 3, u: 3} to form a word, what is the expected number of matches of the pattern 's*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, x: 2, j: 5, p: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 8, p: 4} to form a word, what is the expected number of matches of the pattern 'p+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {x: 8, k: 4}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 3, t: 1, y: 4, k: 4} to form a word, what is the expected number of matches of the pattern 'ya+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 2, z: 5, x: 3, b: 2}, what is the expected number of times the pattern 'xx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 6, p: 6} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 8, k: 4} to form a word, what is the expected number of matches of the pattern 'p+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 5, c: 7}, what is the expected number of times the pattern 'ch*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 3, n: 2, i: 1, r: 2, u: 4}. What is the expected number of occurrences of the pattern 'n*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, a: 2, h: 3, r: 2, i: 1}, what is the expected number of times the pattern 'r*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 3, w: 4, k: 2, y: 1, q: 2}, what is the expected number of times the pattern 'sy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, u: 2, v: 3, d: 1, h: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 3, p: 3, t: 2, r: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 4, d: 4, w: 4} to form a word, what is the expected number of matches of the pattern 'l*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 4, p: 4, c: 4}, what is the expected number of times the pattern 'c+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 5, d: 5, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, u: 2, h: 1, m: 3, d: 3}, what is the expected number of times the pattern 'hu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 2, z: 5, o: 4, a: 1}. What is the expected number of occurrences of the pattern 'a+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 2, l: 2, u: 3, m: 1, n: 4} to form a word, what is the expected number of matches of the pattern 'u.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {m: 3, i: 2, o: 5, e: 2}. What is the expected number of occurrences of the pattern 'm*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 6, c: 6}. What is the expected number of occurrences of the pattern 'cg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 4, b: 2, i: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'hb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 2, g: 2, z: 1, k: 2, m: 5}, what is the expected number of times the pattern 'k+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, o: 4, e: 3, p: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 4, p: 2, z: 2, d: 3, n: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, o: 3, n: 2, g: 2, d: 1}, what is the expected number of times the pattern 'o*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, z: 2, x: 2, f: 5}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {j: 4, t: 3, l: 5} to form a word, what is the expected number of matches of the pattern 'l.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 2, y: 3, k: 6, p: 1}. What is the expected number of occurrences of the pattern 'i.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 5, m: 7} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 2, b: 5, t: 5} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 1, g: 2, j: 9}. What is the expected number of occurrences of the pattern 'jk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 2, r: 5, h: 1, o: 1, f: 3}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 3, u: 9}, what is the expected number of times the pattern 'u.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, t: 1, r: 5, l: 2, p: 2}. What is the expected number of occurrences of the pattern 't+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 4, m: 2, x: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 6, a: 6}, what is the expected number of times the pattern 'a*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {c: 3, y: 4, n: 5} to form a word, what is the expected number of matches of the pattern 'yn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {g: 4, h: 8} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 1, g: 1, c: 4, a: 1, n: 5}, what is the expected number of times the pattern 'g*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.54", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 2, l: 1, k: 4, f: 2, j: 3}, what is the expected number of times the pattern 'j*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 4, m: 2, z: 6} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 4, c: 3, n: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 1, d: 2, y: 3, u: 5, i: 1}, what is the expected number of times the pattern 'yu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 2, n: 4, d: 2, j: 2, g: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {w: 2, d: 1, p: 4, i: 5} to form a word, what is the expected number of matches of the pattern 'p.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 8, o: 4} to form a word, what is the expected number of matches of the pattern 'a*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 3, s: 3, p: 1, n: 5}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {l: 2, h: 2, c: 4, u: 3, a: 1}. What is the expected number of occurrences of the pattern 'l*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {f: 3, k: 3, q: 6} to form a word, what is the expected number of matches of the pattern 'q*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 6, t: 3, n: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 4, j: 6, u: 2}, what is the expected number of times the pattern 'j+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, j: 7}. What is the expected number of occurrences of the pattern 'j.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, b: 2, l: 2, f: 5}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 2, x: 3, s: 5, n: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 7, g: 5} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 4, r: 8} to form a word, what is the expected number of matches of the pattern 'rq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 1, d: 6, e: 5}, what is the expected number of times the pattern 'dt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, a: 5, w: 4}, what is the expected number of times the pattern 'da*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, z: 2, w: 2, d: 2, n: 3}, what is the expected number of times the pattern 'z.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 2, d: 3, w: 3, z: 4}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {s: 2, u: 2, h: 2, f: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 4, v: 2, t: 1, n: 5}. What is the expected number of occurrences of the pattern 'ns+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 3, j: 1, w: 6, q: 2} to form a word, what is the expected number of matches of the pattern 'aj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, q: 8}. What is the expected number of occurrences of the pattern 'qi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {t: 3, i: 1, c: 4, p: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 1, y: 2, a: 4, m: 1, e: 4}. What is the expected number of occurrences of the pattern 'a+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 4, a: 8} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, n: 4, x: 3, t: 2}, what is the expected number of times the pattern 'n+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 1, c: 5, f: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, m: 3, d: 4}. What is the expected number of occurrences of the pattern 'm*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {d: 6, z: 3, g: 3}. What is the expected number of occurrences of the pattern 'gz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 5, n: 4, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 5, b: 7}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, k: 6, s: 3}. What is the expected number of occurrences of the pattern 'k+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 1, t: 4, d: 7} to form a word, what is the expected number of matches of the pattern 'r+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {d: 3, i: 4, r: 1, k: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 4, d: 1, r: 3, y: 2, b: 2}. What is the expected number of occurrences of the pattern 'g+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {g: 6, w: 6}. What is the expected number of occurrences of the pattern 'gw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, e: 2, m: 6}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {k: 2, z: 2, c: 8} to form a word, what is the expected number of matches of the pattern 'z.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 4, g: 2, h: 2, w: 2, l: 2}. What is the expected number of occurrences of the pattern 'g.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {p: 5, c: 3, s: 4} to form a word, what is the expected number of matches of the pattern 'ps+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {y: 2, p: 3, d: 2, v: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'y*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 6, y: 6} to form a word, what is the expected number of matches of the pattern 'yz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, h: 3, r: 6}. What is the expected number of occurrences of the pattern 'o+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 3, e: 3, o: 3, n: 3}. What is the expected number of occurrences of the pattern 'eo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 2, p: 3, e: 4, l: 3}. What is the expected number of occurrences of the pattern 'el*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {n: 5, d: 3, j: 4}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 3, k: 1, a: 3, u: 4, j: 1}, what is the expected number of times the pattern 's+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {f: 4, w: 5, i: 2, r: 1}. What is the expected number of occurrences of the pattern 'i.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, f: 2, a: 4, q: 3}, what is the expected number of times the pattern 'q*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 2, o: 5, c: 4, x: 1}, what is the expected number of times the pattern 'e*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {n: 5, y: 2, h: 5} to form a word, what is the expected number of matches of the pattern 'n.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.84", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, u: 3, r: 1, l: 4, z: 1}. What is the expected number of occurrences of the pattern 'zu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {j: 2, n: 2, b: 2, a: 3, e: 3}. What is the expected number of occurrences of the pattern 'na*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 1, z: 1, q: 4, b: 2, c: 4}, what is the expected number of times the pattern 'z*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 3, j: 9}, what is the expected number of times the pattern 'j.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 3, x: 6, o: 3}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {a: 6, q: 6} to form a word, what is the expected number of matches of the pattern 'qa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 4, z: 3, w: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'f+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 5, q: 7}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 4, h: 2, t: 4, n: 2}, what is the expected number of times the pattern 'x+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {m: 5, d: 1, z: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'u+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 5, g: 7} to form a word, what is the expected number of matches of the pattern 'g*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 1, n: 4, z: 4, a: 3}, what is the expected number of times the pattern 'z.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, q: 3, h: 3, b: 3}. What is the expected number of occurrences of the pattern 'hh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 1, i: 2, v: 1, t: 5, l: 3}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {z: 3, k: 9} to form a word, what is the expected number of matches of the pattern 'k+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, g: 5, j: 4}. What is the expected number of occurrences of the pattern 'g*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 6, v: 4, k: 2}, what is the expected number of times the pattern 'u*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 6, y: 6}, what is the expected number of times the pattern 'u*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {b: 8, e: 4} to form a word, what is the expected number of matches of the pattern 'ee*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {r: 5, g: 3, l: 4} to form a word, what is the expected number of matches of the pattern 'l*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.47", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 9, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {l: 5, r: 5, i: 2} to form a word, what is the expected number of matches of the pattern 'i*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {i: 5, a: 4, c: 3}. What is the expected number of occurrences of the pattern 'ci+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {x: 6, t: 6} to form a word, what is the expected number of matches of the pattern 't.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {q: 4, j: 4, y: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'y+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {b: 3, l: 4, t: 2, s: 2, f: 1}. What is the expected number of occurrences of the pattern 'f*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {o: 2, e: 6, q: 4} to form a word, what is the expected number of matches of the pattern 'o*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 2, b: 4, m: 6}, what is the expected number of times the pattern 'ee+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {u: 6, b: 3, z: 3}. What is the expected number of occurrences of the pattern 'zb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 6 letters from the multiset {e: 4, q: 8} to form a word, what is the expected number of matches of the pattern 'eq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, i: 2, h: 6, u: 1}. What is the expected number of occurrences of the pattern 'i*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}