{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, x: 2, v: 3, y: 2, l: 1}, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 6, u: 3} 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": "3.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 2, j: 2, l: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'c+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 3, q: 3, a: 1, x: 2}, what is the expected number of times the pattern 'jx+' 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 4 letters from the multiset {h: 6, u: 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, r: 2, s: 1, j: 2, g: 2}, what is the expected number of times the pattern 't.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, n: 4, p: 2}, what is the expected number of times the pattern 'n+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 3, t: 3, a: 3}, 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 2, x: 1, d: 2, q: 2, s: 2}, what is the expected number of times the pattern 'qf*' 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 4 letters from the multiset {i: 2, l: 3, k: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'i.*k'? 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 4 letters from the multiset {a: 3, i: 6}. What is the expected number of occurrences of the pattern 'i*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": "2.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 2, f: 2, c: 2, u: 2, d: 1}. What is the expected number of occurrences of the pattern 'd.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 2, t: 1, f: 1, o: 1, x: 4}. What is the expected number of occurrences of the pattern 'fo+' 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": "Form a word by randomly choosing 4 letters from the multiset {r: 4, e: 3, z: 2}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 3, g: 6}. What is the expected number of occurrences of the pattern 'gl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, w: 1, t: 3, r: 3}, what is the expected number of times the pattern 'p*w' 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 4 by randomly selecting letters from the multiset {f: 4, h: 2, c: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 3, l: 4, s: 2} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 4, t: 3, k: 1, x: 1}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, v: 1, b: 3, k: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, z: 2, j: 3, d: 1, i: 1}. What is the expected number of occurrences of the pattern 'i+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": "0.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, y: 1, w: 2, v: 1, t: 2}, what is the expected number of times the pattern 'v+y' appears? 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": "When randomly selecting 4 letters from the multiset {v: 2, h: 3, t: 1, f: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'hv+'? 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 4 letters from the multiset {q: 5, u: 4} to form a word, what is the expected number of matches of the pattern 'q*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 1, v: 4, r: 2, j: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 5, r: 4} to form a word, what is the expected number of matches of the pattern 'zr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 1, e: 2, i: 2, r: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, p: 4, r: 1, l: 2}, what is the expected number of times the pattern 'l.*b' 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 4 by randomly selecting letters from the multiset {r: 3, q: 2, l: 3, v: 1}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, y: 4, f: 2, j: 1}, 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": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 4, t: 2, x: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 4, o: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'm*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 5, d: 4}. 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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, q: 1, o: 1, j: 3, p: 2}, what is the expected number of times the pattern 'qj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, l: 7}, what is the expected number of times the pattern 's+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, o: 4, n: 2}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, n: 3, x: 1, b: 3, r: 1}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 2, n: 2, c: 3, p: 1, b: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, i: 4, y: 2}. 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, p: 2, j: 3, s: 2}. 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": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, q: 2, w: 2, y: 2}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 5, y: 1, z: 3}, 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": "1.46", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 6, q: 3}, what is the expected number of times the pattern 'q+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 4, j: 5}, what is the expected number of times the pattern 'j.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 4, l: 2, o: 1, p: 2}. What is the expected number of occurrences of the pattern 'o+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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 2, n: 3, f: 2, r: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 1, b: 2, t: 2, i: 2, a: 2}. What is the expected number of occurrences of the pattern 'am*' 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 4 by randomly selecting letters from the multiset {o: 7, j: 2}, 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 6, r: 1, a: 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": "0.55", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 3, u: 6} 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 1, a: 1, s: 2, n: 3, m: 2}, what is the expected number of times the pattern 'ln+' appears? 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": "Form a word by randomly choosing 4 letters from the multiset {d: 3, x: 1, u: 1, c: 1, l: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 1, j: 1, k: 2, y: 5} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 2, j: 1, t: 5, y: 1}. What is the expected number of occurrences of the pattern 'a*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": "2.68", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, a: 1, z: 1, g: 2, f: 2}. What is the expected number of occurrences of the pattern 'gp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 1, t: 1, f: 1, v: 3, u: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, l: 3, q: 2, k: 1, o: 2}, what is the expected number of times the pattern 'o*k' 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 4 by randomly selecting letters from the multiset {k: 7, o: 2}, what is the expected number of times the pattern 'o.*k' 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": "Form a word by randomly choosing 4 letters from the multiset {a: 3, i: 2, t: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 2, e: 1, u: 2, s: 3, a: 1}, what is the expected number of times the pattern 'e+u' 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 4 letters from the multiset {i: 3, z: 6} to form a word, what is the expected number of matches of the pattern 'z.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, a: 6}, what is the expected number of times the pattern 'ca*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, p: 6, l: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 3, u: 3, z: 2, i: 1}, what is the expected number of times the pattern 's*u' appears? Round 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 4 letters from the multiset {o: 3, m: 3, f: 3}. What is the expected number of occurrences of the pattern 'mf+' 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 4 letters from the multiset {r: 3, o: 2, z: 1, b: 3}. What is the expected number of occurrences of the pattern 'oo*' 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 4 letters from the multiset {v: 4, d: 5}. What is the expected number of occurrences of the pattern 'vd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, f: 2, h: 1, z: 1, g: 1}. What is the expected number of occurrences of the pattern 'z.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 1, g: 4, e: 2, c: 2}. What is the expected number of occurrences of the pattern 'e+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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, w: 1, l: 3, y: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, c: 5, h: 1}. What is the expected number of occurrences of the pattern 'c+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": "0.92", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 5, o: 4}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, j: 2, b: 1, z: 2, y: 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 1, b: 1, t: 2, p: 2, z: 3} to form a word, what is the expected number of matches of the pattern 'z+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 5, f: 4} to form a word, what is the expected number of matches of the pattern 'f*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 5, l: 4}. 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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 5, r: 4}, what is the expected number of times the pattern 'zr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 4, l: 3, q: 2} to form a word, what is the expected number of matches of the pattern 'lb+'? 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": "When randomly selecting 4 letters from the multiset {u: 2, z: 3, n: 1, w: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 5, y: 2, g: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 5, i: 4}. What is the expected number of occurrences of the pattern 'v+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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 1, s: 2, p: 2, r: 2, i: 2}, what is the expected number of times the pattern 'pr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, a: 4, l: 2, j: 1, q: 1}. What is the expected number of occurrences of the pattern 'qa*' 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": "Form a word by randomly choosing 4 letters from the multiset {j: 2, z: 3, i: 2, t: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 5, j: 4}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 2, f: 4, a: 1, q: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'ue+'? 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 4 letters from the multiset {h: 1, e: 1, s: 3, u: 1, m: 3}. What is the expected number of occurrences of the pattern 'e.*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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 1, k: 4, s: 1, a: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'a+s'? 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 4 letters from the multiset {h: 2, a: 4, y: 1, t: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 7, f: 2} to form a word, what is the expected number of matches of the pattern 'j*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 4, p: 5}, what is the expected number of times the pattern 'rp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, a: 4, i: 1, y: 1, x: 1}, what is the expected number of times the pattern 'a+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, g: 2, z: 2, a: 2, p: 1}, what is the expected number of times the pattern 'p.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, s: 2, l: 2, z: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 4, y: 2, b: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 5, s: 1, f: 2, g: 1}. What is the expected number of occurrences of the pattern 'i*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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 5, n: 3, q: 1}. 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": "1.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 2, t: 1, y: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'z.*y'? 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": "Form a word by randomly choosing 4 letters from the multiset {o: 3, u: 2, a: 2, c: 2}. What is the expected number of occurrences of the pattern 'a.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, x: 5}, what is the expected number of times the pattern 'x+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, a: 2, x: 2, i: 2}. What is the expected number of occurrences of the pattern 'i+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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 3, o: 6}, what is the expected number of times the pattern 'l*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, t: 2, m: 2, l: 1, c: 2}, what is the expected number of times the pattern 'tc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, z: 4, a: 2, m: 1}, what is the expected number of times the pattern 'cm+' 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 4 letters from the multiset {a: 3, h: 2, k: 2, v: 2} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 3, h: 6}. What is the expected number of occurrences of the pattern 'h.*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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 1, j: 2, h: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*h'? 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 4 by randomly selecting letters from the multiset {z: 2, q: 3, u: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 4, c: 4, m: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 2, b: 2, p: 2, z: 3} to form a word, what is the expected number of matches of the pattern 'lb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 6, b: 2, c: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, v: 3, e: 2, s: 1}, what is the expected number of times the pattern 'se*' 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 4 by randomly selecting letters from the multiset {p: 1, w: 4, u: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 3, t: 3, u: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 2, s: 4, k: 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": "2.38", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 1, c: 2, h: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'c*h'? 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 4 letters from the multiset {m: 2, h: 1, i: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'ma+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, s: 4, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 2, o: 2, f: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'fs*'? 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 4 letters from the multiset {a: 8, k: 1}. What is the expected number of occurrences of the pattern 'k.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, s: 3, r: 2, h: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, x: 3, j: 2}, what is the expected number of times the pattern 'tx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, h: 5}. What is the expected number of occurrences of the pattern 'jh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 1, h: 2, y: 2, a: 1, s: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, a: 2, f: 1, x: 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": "When randomly selecting 4 letters from the multiset {e: 1, j: 2, s: 2, z: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'j*z'? 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 4 letters from the multiset {n: 3, v: 6} to form a word, what is the expected number of matches of the pattern 'n.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 4, z: 5}. 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": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 4, n: 3, g: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 5, v: 4}. What is the expected number of occurrences of the pattern 'v.*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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 2, b: 2, q: 2, p: 3} 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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 3, p: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'e.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, n: 2, j: 5} to form a word, what is the expected number of matches of the pattern 'mj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 3, d: 3, c: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, q: 3, n: 3, r: 2}. What is the expected number of occurrences of the pattern 'r+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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 4, y: 3, g: 2} 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, a: 3, p: 2, h: 3}. What is the expected number of occurrences of the pattern 'xp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 4, i: 2, v: 1, a: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'i+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 1, j: 1, z: 3, q: 4}, what is the expected number of times the pattern 'j*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, f: 3, l: 4}, what is the expected number of times the pattern 'f.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 3, h: 1, a: 1, k: 1, f: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 3, v: 6} to form a word, what is the expected number of matches of the pattern 'v*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 2, d: 1, p: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'pg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 2, u: 2, x: 2, v: 2, f: 1}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 4, h: 5}, what is the expected number of times the pattern 'hc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, t: 1, m: 3, k: 1, q: 3}, what is the expected number of times the pattern 'tc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, q: 2, d: 1, g: 3}. What is the expected number of occurrences of the pattern 'k+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": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 1, w: 5, e: 2, r: 1}. What is the expected number of occurrences of the pattern 'r.*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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 4, o: 1, z: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n*o'? 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 4 letters from the multiset {i: 2, v: 3, z: 4} 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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 3, y: 2, i: 4}, what is the expected number of times the pattern 'y*i' 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 4 letters from the multiset {k: 4, z: 5}. What is the expected number of occurrences of the pattern 'kz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 7, e: 2}, what is the expected number of times the pattern 'ce+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 3, h: 6}. 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, o: 7}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, f: 2, v: 2, r: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 2, v: 1, g: 4, b: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 3, n: 1, x: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'js+'? 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 4 letters from the multiset {o: 4, x: 5} to form a word, what is the expected number of matches of the pattern 'o*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 3, p: 2, d: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'pd*'? 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 4 letters from the multiset {h: 1, f: 3, a: 2, w: 1, s: 2} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, a: 3, t: 4}. What is the expected number of occurrences of the pattern 'dt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 3, r: 6}. What is the expected number of occurrences of the pattern 'fr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, u: 1, c: 2, b: 1, s: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 1, k: 1, z: 3, y: 2, h: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, x: 1, d: 1, y: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'x*q'? 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 4 letters from the multiset {p: 1, j: 3, m: 1, z: 3, q: 1} 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": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 6, z: 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": "2.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 2, k: 2, p: 2, r: 1, o: 2}. What is the expected number of occurrences of the pattern 'o*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": "0.54", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 3, i: 3, q: 2, e: 1} 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, n: 1, t: 2, e: 3, u: 1}, what is the expected number of times the pattern 'e.*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 4 letters from the multiset {x: 6, f: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 3, k: 2, w: 3, v: 1}, what is the expected number of times the pattern 'w*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 1, c: 2, r: 2, x: 3, a: 1}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, p: 1, f: 6, l: 1}, 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": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 3, h: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'v*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, m: 5, l: 3}. What is the expected number of occurrences of the pattern 'm*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": "2.26", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, s: 3, l: 2, p: 2, o: 1}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, g: 3, q: 2, k: 2}. What is the expected number of occurrences of the pattern 'kg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, z: 7}, 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, k: 6}, what is the expected number of times the pattern 'vk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, s: 2, p: 2, o: 2, 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 2, x: 1, d: 3, f: 1, g: 2} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 1, u: 2, c: 3, b: 1, q: 2} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 1, d: 2, u: 3, p: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, v: 2, i: 5}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 3, u: 6} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 3, m: 1, j: 1, q: 1, l: 3}. What is the expected number of occurrences of the pattern 'm.*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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, g: 6, l: 1}, what is the expected number of times the pattern 'gl+' 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 4 letters from the multiset {e: 1, y: 2, l: 2, d: 1, n: 3}. What is the expected number of occurrences of the pattern 'e.*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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 5, y: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 3, d: 5, o: 1} to form a word, what is the expected number of matches of the pattern 'r.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 4, f: 3, n: 2}. What is the expected number of occurrences of the pattern 'f+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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 6, t: 3}, 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 2, e: 7} to form a word, what is the expected number of matches of the pattern 'er+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 4, s: 5}. What is the expected number of occurrences of the pattern 'd.*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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 4, q: 5} 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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 5, i: 4} to form a word, what is the expected number of matches of the pattern 'm+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, y: 4, p: 3}, what is the expected number of times the pattern 'yp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 1, j: 2, c: 2, d: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'de*'? 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 4 letters from the multiset {e: 2, o: 4, c: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'eo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 2, g: 2, n: 5}. What is the expected number of occurrences of the pattern 'v+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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, r: 2, s: 4} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 3, a: 1, l: 4, r: 1} to form a word, what is the expected number of matches of the pattern 'lr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, c: 1, j: 2, w: 2, n: 2}, what is the expected number of times the pattern 'n.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 5, w: 4} 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, k: 4, i: 1}, what is the expected number of times the pattern 'a+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 2, h: 2, l: 2, w: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'l*x'? 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 4 letters from the multiset {c: 3, t: 1, k: 2, s: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, q: 3, i: 4}. What is the expected number of occurrences of the pattern 'iu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 2, y: 7} to form a word, what is the expected number of matches of the pattern 'cy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, m: 2, n: 3, u: 2}. What is the expected number of occurrences of the pattern 'mn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 5, y: 4}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 6, s: 3}, what is the expected number of times the pattern 's+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 3, k: 2, l: 3, f: 1}. What is the expected number of occurrences of the pattern 'l.*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": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 1, j: 3, t: 2, i: 2, s: 1}, what is the expected number of times the pattern 's+j' 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 4 letters from the multiset {a: 4, n: 5}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 1, p: 1, a: 1, o: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'a*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 1, c: 3, r: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'i*r'? 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 4 by randomly selecting letters from the multiset {g: 2, w: 3, t: 1, m: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, h: 3, l: 4}, what is the expected number of times the pattern 'l*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, r: 3, p: 2}, what is the expected number of times the pattern 'p.*l' appears? 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 4 by randomly selecting letters from the multiset {k: 4, d: 3, w: 2}, what is the expected number of times the pattern 'w.*k' appears? 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": "When randomly selecting 4 letters from the multiset {o: 2, g: 2, u: 1, p: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'pg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, v: 2, m: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'ip*'? 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": "When randomly selecting 4 letters from the multiset {y: 2, d: 1, q: 4, s: 2} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 6, v: 3} to form a word, what is the expected number of matches of the pattern 'v+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, q: 4, e: 3}. What is the expected number of occurrences of the pattern 'q.*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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, o: 5}, what is the expected number of times the pattern 'q.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, f: 3, m: 3, x: 2}, what is the expected number of times the pattern 'ix+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 7, i: 2}, what is the expected number of times the pattern 'i*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 2, c: 2, u: 1, r: 3, a: 1} to form a word, what is the expected number of matches of the pattern 'u+a'? 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": "When randomly selecting 4 letters from the multiset {e: 2, y: 2, m: 1, x: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'mu*'? 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 4 by randomly selecting letters from the multiset {y: 4, n: 1, r: 2, j: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 3, v: 6}, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, u: 5}, what is the expected number of times the pattern 'l+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 1, l: 2, g: 3, b: 3} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 2, t: 1, j: 1, k: 3, s: 2} to form a word, what is the expected number of matches of the pattern 't+v'? 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 4 letters from the multiset {o: 2, n: 2, t: 1, v: 2, g: 2} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, w: 6}, what is the expected number of times the pattern 'w+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 2, l: 2, o: 1, b: 2, u: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 1, p: 2, a: 2, j: 1, i: 3}. What is the expected number of occurrences of the pattern 'p+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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, m: 2, d: 3, e: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 4, s: 1, m: 2, y: 1, p: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 2, r: 2, t: 3, q: 2}. What is the expected number of occurrences of the pattern 'm*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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 4, f: 3, u: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 4, w: 3, m: 2}. What is the expected number of occurrences of the pattern 'm+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": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, s: 2, p: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*s'? Round 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 4 letters from the multiset {p: 2, b: 1, y: 5, n: 1}. What is the expected number of occurrences of the pattern 'p+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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, o: 7}, what is the expected number of times the pattern 'to*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 4, e: 5}, 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, a: 4, m: 1, o: 2}, 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 2, l: 5, t: 2} 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, a: 7}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 3, b: 1, p: 3, h: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 4, y: 5}, what is the expected number of times the pattern 'yz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 5, p: 2, b: 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": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 3, w: 6} 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, p: 2, g: 2, i: 2, x: 1}, what is the expected number of times the pattern 'gq*' 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 4 letters from the multiset {h: 4, d: 5} to form a word, what is the expected number of matches of the pattern 'd+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 1, x: 1, q: 3, s: 2, l: 2}. 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": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 5, b: 4}, what is the expected number of times the pattern 'n.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, p: 7}. 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 3, d: 3, m: 3}. What is the expected number of occurrences of the pattern 'd*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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 3, d: 1, w: 5}, what is the expected number of times the pattern 'dr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, u: 3, d: 2}. What is the expected number of occurrences of the pattern 'd+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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 3, m: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'c.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 1, x: 2, d: 3, u: 1, v: 2}. What is the expected number of occurrences of the pattern 'n+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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, s: 1, k: 5, d: 2}. What is the expected number of occurrences of the pattern 'k*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": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 4, l: 1, n: 1, a: 2, p: 1}. What is the expected number of occurrences of the pattern 't.*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": "Form a word by randomly choosing 4 letters from the multiset {k: 2, e: 1, f: 1, a: 3, w: 2}. 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 2, k: 2, v: 1, y: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'v.*d'? 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 4 by randomly selecting letters from the multiset {r: 2, z: 3, o: 4}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 4, j: 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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, s: 3, n: 1, l: 2}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, u: 5, c: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 4, y: 2, q: 2, n: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 5, d: 4}. What is the expected number of occurrences of the pattern 'd+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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 3, m: 6}. What is the expected number of occurrences of the pattern 'm.*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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 5, i: 4}. What is the expected number of occurrences of the pattern 'i*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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, w: 2, j: 2, g: 2}. What is the expected number of occurrences of the pattern 'w.*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 4 letters from the multiset {i: 2, v: 5, b: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, u: 3, n: 1, c: 4}. What is the expected number of occurrences of the pattern 'wn+' 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": "Form a word by randomly choosing 4 letters from the multiset {x: 6, z: 3}. 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 1, b: 3, y: 2, z: 1, o: 2}, 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": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 7, j: 2}, 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, r: 1, w: 2, c: 1, j: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 4, z: 5} 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": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 4, d: 3, c: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, s: 1, e: 2, g: 2}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, j: 3, f: 3, c: 1}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, m: 1, w: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'qm+'? 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 4 letters from the multiset {y: 3, h: 2, v: 1, c: 1, g: 2} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 7, l: 2}, what is the expected number of times the pattern 'v.*l' 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 4 by randomly selecting letters from the multiset {i: 1, x: 3, k: 1, g: 3, z: 1}, what is the expected number of times the pattern 'g.*k' 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 4 letters from the multiset {i: 4, m: 5} to form a word, what is the expected number of matches of the pattern 'im*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 5, o: 4}. What is the expected number of occurrences of the pattern 'mo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, a: 1, q: 3, u: 3}. What is the expected number of occurrences of the pattern 'lu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 1, j: 2, n: 1, a: 3, g: 2} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, u: 2, d: 2, h: 2, c: 1}, what is the expected number of times the pattern 'd.*u' 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 4 by randomly selecting letters from the multiset {s: 2, x: 4, m: 3}, what is the expected number of times the pattern 's.*x' appears? 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": "Form a word by randomly choosing 4 letters from the multiset {p: 1, s: 4, k: 4}. What is the expected number of occurrences of the pattern 'ks+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.89", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, l: 1, d: 2, u: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'ym+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 2, h: 2, x: 3, v: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 3, r: 2, j: 1, x: 2, m: 1}. What is the expected number of occurrences of the pattern 'm.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 2, w: 1, f: 3, l: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'hw*'? 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 4 by randomly selecting letters from the multiset {z: 4, u: 5}, what is the expected number of times the pattern 'z*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, y: 3, b: 2, o: 1} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, d: 5, j: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 4, j: 1, q: 4} to form a word, what is the expected number of matches of the pattern 'fj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, m: 1, b: 1, j: 4}, what is the expected number of times the pattern 'uj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 2, l: 5, t: 2}, what is the expected number of times the pattern 't+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 1, t: 3, m: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'jm*'? 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 4 letters from the multiset {u: 5, o: 4} to form a word, what is the expected number of matches of the pattern 'u*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, p: 4, w: 3}. What is the expected number of occurrences of the pattern 'd+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": "Form a word by randomly choosing 4 letters from the multiset {t: 5, s: 2, i: 2}. What is the expected number of occurrences of the pattern 's+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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 3, c: 1, d: 5} to form a word, what is the expected number of matches of the pattern 'cd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.31", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 3, i: 6}, what is the expected number of times the pattern 'i+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 1, t: 3, e: 1, r: 3, k: 1} 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": "Form a word by randomly choosing 4 letters from the multiset {l: 1, h: 3, q: 2, t: 2, f: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 5, c: 4}, what is the expected number of times the pattern 'xc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 3, f: 3, h: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'o.*f'? Round 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 4 letters from the multiset {l: 2, v: 3, z: 4} to form a word, what is the expected number of matches of the pattern 'zv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, p: 4}. What is the expected number of occurrences of the pattern 'p*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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, g: 2, d: 2, j: 1}. What is the expected number of occurrences of the pattern 'g+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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 3, m: 1, h: 3, s: 1, f: 1}. 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, s: 5, m: 3}, what is the expected number of times the pattern 'g+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 1, m: 2, y: 2, x: 1, l: 3} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 2, x: 2, y: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'x+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 4, g: 5}, what is the expected number of times the pattern 'g.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, t: 5}. What is the expected number of occurrences of the pattern 'x*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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 6, c: 3}, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 5, r: 2, b: 2}. 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 4, d: 2, j: 3} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 3, z: 6}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, c: 2, u: 2, k: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 2, m: 2, p: 3, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 3, f: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'op*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 3, f: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'f*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 6, m: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, n: 4, y: 2, s: 1}, what is the expected number of times the pattern 'yg*' 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 4 letters from the multiset {j: 3, a: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'da+'? 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 4 by randomly selecting letters from the multiset {k: 5, x: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, w: 2, l: 3, i: 1}, what is the expected number of times the pattern 'wq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 3, n: 3, x: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r+n'? 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 4 letters from the multiset {q: 6, b: 3}. What is the expected number of occurrences of the pattern 'q.*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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 5, k: 4}. What is the expected number of occurrences of the pattern 'kr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 1, r: 3, i: 1, e: 3, c: 1}, what is the expected number of times the pattern 'ir+' appears? 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 4 letters from the multiset {t: 3, x: 2, n: 1, i: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'qn+'? 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 4 by randomly selecting letters from the multiset {k: 5, m: 4}, 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": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 2, z: 2, p: 2, b: 2, d: 1}. What is the expected number of occurrences of the pattern 'yb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, u: 3, s: 2, e: 2}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 4, s: 2, y: 1, m: 1, u: 1}. What is the expected number of occurrences of the pattern 'y*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": "0.49", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, f: 2, y: 3, l: 2}. What is the expected number of occurrences of the pattern 'yf+' 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 4 letters from the multiset {o: 2, v: 2, a: 3, h: 2}. What is the expected number of occurrences of the pattern 'v*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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 3, r: 3, y: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 2, p: 2, f: 2, y: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'op*'? 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 4 letters from the multiset {f: 2, u: 4, a: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'ah*'? 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": "Form a word by randomly choosing 4 letters from the multiset {q: 3, a: 2, f: 1, e: 3}. 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, f: 1, s: 2, a: 2, v: 2}, 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, z: 1, v: 2, p: 1, f: 4}, what is the expected number of times the pattern 'zv*' 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 4 by randomly selecting letters from the multiset {t: 4, n: 1, x: 4}, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 5, e: 4} to form a word, what is the expected number of matches of the pattern 'e*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 2, u: 2, s: 3, r: 2} 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": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 2, s: 3, v: 2, x: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, v: 4, j: 2}. What is the expected number of occurrences of the pattern 'xv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 1, i: 5, x: 3}, 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": "0.42", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 6, w: 3}, what is the expected number of times the pattern 'vw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 3, a: 2, w: 3, n: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, d: 5}, what is the expected number of times the pattern 'q.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 4, w: 5}. What is the expected number of occurrences of the pattern 'wa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 4, v: 5}, what is the expected number of times the pattern 'u*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 5, t: 4}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, e: 2, s: 4}, what is the expected number of times the pattern 'se+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 6, t: 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": "3.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 4, w: 3, n: 2}, what is the expected number of times the pattern 'ww*' 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": "When randomly selecting 4 letters from the multiset {c: 3, n: 3, t: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 5, i: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'f+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 1, w: 3, p: 3, y: 2}. What is the expected number of occurrences of the pattern 'y*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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 2, u: 2, e: 1, m: 4} to form a word, what is the expected number of matches of the pattern 'e*u'? 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 4 letters from the multiset {d: 2, e: 2, o: 5}. What is the expected number of occurrences of the pattern 'oe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 1, t: 1, p: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'rt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, z: 4, e: 3}. What is the expected number of occurrences of the pattern 'e.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, s: 1, p: 1, k: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, n: 3, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 2, e: 1, i: 2, n: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'ex+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, n: 3, v: 1, z: 1, o: 2}. What is the expected number of occurrences of the pattern 'r*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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 1, z: 4, n: 4}, what is the expected number of times the pattern 'n+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.89", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 4, y: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'mp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, i: 6, q: 1}. 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": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 6, f: 3}. What is the expected number of occurrences of the pattern 'f.*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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, y: 1, d: 4}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 2, w: 1, l: 1, p: 3, d: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, m: 1, z: 1, p: 1, k: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 1, r: 2, a: 2, n: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'nu*'? 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 4 letters from the multiset {i: 1, y: 3, e: 5}. What is the expected number of occurrences of the pattern 'iy+' 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 4 by randomly selecting letters from the multiset {n: 4, a: 5}, what is the expected number of times the pattern 'an+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 2, y: 1, s: 2, l: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'd*y'? 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 4 by randomly selecting letters from the multiset {h: 5, l: 4}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, x: 4, p: 3, k: 1}, what is the expected number of times the pattern 'pk+' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, s: 2, q: 3}, 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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 3, o: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'o+k'? 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 4 letters from the multiset {o: 2, j: 2, g: 2, y: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'j*y'? 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": "Form a word by randomly choosing 4 letters from the multiset {c: 2, m: 7}. What is the expected number of occurrences of the pattern 'm*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": "1.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 4, n: 1, a: 4}, what is the expected number of times the pattern 'na+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 2, v: 1, s: 3, r: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'vw+'? 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 4 letters from the multiset {r: 2, q: 5, o: 2}. What is the expected number of occurrences of the pattern 'o*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": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, m: 6}, what is the expected number of times the pattern 'em+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, v: 4, b: 1, c: 3} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, c: 2, x: 1, b: 3, f: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, s: 1, r: 3, m: 1, i: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 3, m: 1, q: 2, r: 2, x: 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": "When randomly selecting 4 letters from the multiset {z: 5, s: 4} 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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, r: 4, q: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, k: 2, b: 1, g: 2, e: 1}. What is the expected number of occurrences of the pattern 'k+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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, e: 3, w: 1, h: 1, l: 1} 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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, s: 2, x: 5}. What is the expected number of occurrences of the pattern 'g+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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 3, k: 1, u: 2, j: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'k.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, m: 5, e: 1}. What is the expected number of occurrences of the pattern 'em*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 5, g: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 1, o: 4, w: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'm.*g'? 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 4 letters from the multiset {o: 5, y: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'yo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, g: 2, j: 3, q: 3}. What is the expected number of occurrences of the pattern 'v+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": "When randomly selecting 4 letters from the multiset {s: 3, a: 1, j: 1, q: 1, x: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, s: 4, j: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 5, y: 4} to form a word, what is the expected number of matches of the pattern 'yc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, p: 4, t: 3} to form a word, what is the expected number of matches of the pattern 'tp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 5, r: 4} to form a word, what is the expected number of matches of the pattern 'e+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 3, g: 2, i: 4}, what is the expected number of times the pattern 'im+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, o: 2, p: 1, n: 3, g: 2}, what is the expected number of times the pattern 'ot*' 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 4 letters from the multiset {j: 4, h: 4, b: 1}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, l: 2, t: 2, m: 1}, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, d: 3, f: 2, u: 2}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 3, g: 3, j: 3}. What is the expected number of occurrences of the pattern 'l.*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": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, p: 1, k: 1, s: 3, b: 1}, what is the expected number of times the pattern 'k*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 3, s: 2, u: 2, t: 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 6, v: 3}, what is the expected number of times the pattern 'v*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 6, h: 3} to form a word, what is the expected number of matches of the pattern 'wh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, r: 1, f: 2, v: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 2, i: 1, s: 1, o: 2, d: 3}. What is the expected number of occurrences of the pattern 'i.*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": "Form a word by randomly choosing 4 letters from the multiset {r: 2, v: 3, j: 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 5, h: 4} 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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 2, y: 5, e: 2}. What is the expected number of occurrences of the pattern 'v.*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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 5, k: 4} to form a word, what is the expected number of matches of the pattern 'ke*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 4, r: 1, x: 1, c: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'w+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 3, c: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'zc+'? 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": "When randomly selecting 4 letters from the multiset {i: 1, d: 2, w: 2, z: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'ld*'? 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 4 letters from the multiset {b: 3, c: 3, x: 2, s: 1}. 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": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 3, b: 2, v: 4}. What is the expected number of occurrences of the pattern 'w.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, s: 5, f: 1, l: 1}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, n: 3, w: 2, b: 2}, what is the expected number of times the pattern 'wn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 1, s: 2, u: 1, k: 2, r: 3}, what is the expected number of times the pattern 'u+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 4 letters from the multiset {d: 1, r: 4, i: 1, o: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 3, x: 3, l: 3}. What is the expected number of occurrences of the pattern 'ly+' 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 4 letters from the multiset {h: 2, j: 1, a: 1, y: 2, i: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 2, h: 2, s: 1, j: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'j*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 1, b: 1, s: 1, h: 2, o: 4}. What is the expected number of occurrences of the pattern 'cb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 2, k: 2, i: 2, s: 1, h: 2} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, v: 1, a: 2, w: 1, h: 2}, what is the expected number of times the pattern 'wt+' appears? 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": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 4, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, f: 7}, what is the expected number of times the pattern 'fs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 1, n: 5, b: 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 4 by randomly selecting letters from the multiset {a: 5, x: 4}, what is the expected number of times the pattern 'x+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, h: 4, n: 4} to form a word, what is the expected number of matches of the pattern 'nh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, q: 4, u: 2, l: 2}. What is the expected number of occurrences of the pattern 'ux*' 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 4 letters from the multiset {r: 3, b: 1, h: 4, n: 1}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 2, n: 1, w: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'w+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 2, h: 1, t: 4, b: 2} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, p: 4, x: 2, q: 1}. What is the expected number of occurrences of the pattern 'dq+' 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 4 by randomly selecting letters from the multiset {o: 2, y: 1, e: 3, f: 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": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, o: 3, f: 4}, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, x: 2, o: 3, e: 2}. What is the expected number of occurrences of the pattern 'f*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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 1, g: 4, a: 1, e: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'ge+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, v: 2, d: 2, l: 2, q: 2}, what is the expected number of times the pattern 'cq*' 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 4 by randomly selecting letters from the multiset {f: 1, u: 5, i: 3}, what is the expected number of times the pattern 'u.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.42", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 1, p: 4, s: 1, u: 3}, what is the expected number of times the pattern 'su*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, b: 1, r: 1, t: 4}. What is the expected number of occurrences of the pattern 'e.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, b: 2, g: 1, u: 1, h: 4}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, q: 2, v: 1, u: 4}. What is the expected number of occurrences of the pattern 'q.*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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, v: 7}. What is the expected number of occurrences of the pattern 'v.*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": "1.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 2, m: 1, t: 1, x: 3, z: 2}, what is the expected number of times the pattern 'ot+' 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 4 letters from the multiset {v: 3, w: 2, l: 1, x: 1, o: 2}. What is the expected number of occurrences of the pattern 'vl+' 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 4 by randomly selecting letters from the multiset {n: 5, f: 4}, what is the expected number of times the pattern 'fn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, v: 3, a: 4} to form a word, what is the expected number of matches of the pattern 'va+'? 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 4 by randomly selecting letters from the multiset {n: 3, c: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 1, x: 2, o: 2, c: 2, q: 2}, 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 1, r: 2, k: 4, y: 1, q: 1}, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 3, l: 6}, what is the expected number of times the pattern 'l.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, d: 6}, what is the expected number of times the pattern 'z.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, m: 3, s: 1, r: 2}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, b: 2, p: 1, z: 1, l: 2}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, d: 4}. 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 2, u: 3, l: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'uz*'? 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 4 letters from the multiset {l: 6, t: 3}. What is the expected number of occurrences of the pattern 't+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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, o: 2, y: 2, z: 2, u: 2}, what is the expected number of times the pattern 'y*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": "Form a word by randomly choosing 4 letters from the multiset {r: 5, w: 4}. What is the expected number of occurrences of the pattern 'wr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, p: 3, b: 1, w: 1, d: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, n: 3, o: 4}. What is the expected number of occurrences of the pattern 'n+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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, m: 2, z: 1, c: 4}, what is the expected number of times the pattern 'm+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 2, f: 2, x: 1, q: 4} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 7, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*f'? 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 4 letters from the multiset {h: 2, k: 2, w: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'w+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, u: 1, d: 2, n: 2, z: 1}. What is the expected number of occurrences of the pattern 'z+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 4 letters from the multiset {d: 2, k: 4, m: 3}. What is the expected number of occurrences of the pattern 'd+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": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, u: 1, d: 1, w: 1, p: 4}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 3, s: 1, e: 1, a: 3, z: 1}. What is the expected number of occurrences of the pattern 'as+' 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 4 letters from the multiset {d: 6, f: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 4, p: 2, y: 3}. What is the expected number of occurrences of the pattern 'p.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 4, i: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 2, b: 2, i: 3, d: 2}, what is the expected number of times the pattern 'wi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 3, e: 1, v: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'eh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, h: 2, e: 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 2, y: 2, r: 2, h: 1, c: 2} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 5, c: 4} to form a word, what is the expected number of matches of the pattern 'cz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 5, r: 4} to form a word, what is the expected number of matches of the pattern 'rg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 2, s: 2, j: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'i*j'? 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 4 letters from the multiset {l: 3, p: 3, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, c: 4, a: 2, j: 1}, what is the expected number of times the pattern 'j*a' 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 4 by randomly selecting letters from the multiset {k: 3, a: 1, o: 1, p: 3, h: 1}, what is the expected number of times the pattern 'a.*h' 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 4 letters from the multiset {h: 3, n: 6} to form a word, what is the expected number of matches of the pattern 'hn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 4, s: 5}, 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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, e: 2, v: 5}. What is the expected number of occurrences of the pattern 'e.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 1, c: 2, v: 3, n: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'v+k'? 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 4 letters from the multiset {e: 2, w: 3, d: 2, o: 2} 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 2, e: 1, n: 2, w: 4}. What is the expected number of occurrences of the pattern 've+' 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 4 letters from the multiset {y: 4, p: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'x+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 6, v: 3}, what is the expected number of times the pattern 'pv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 1, g: 1, d: 2, h: 2, x: 3}. 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": "0.54", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, w: 7}. What is the expected number of occurrences of the pattern 'x+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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 1, a: 3, u: 4, q: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, y: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 3, e: 2, w: 1, z: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'v+m'? 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 4 by randomly selecting letters from the multiset {q: 3, u: 3, h: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 5, j: 3, w: 1}. What is the expected number of occurrences of the pattern 'w*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": "1.46", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 3, l: 5, m: 1}, what is the expected number of times the pattern 'lo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, s: 1, a: 1, g: 3, w: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, p: 1, y: 2, o: 3, t: 2}, what is the expected number of times the pattern 'tm*' 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 4 by randomly selecting letters from the multiset {f: 4, b: 2, k: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, y: 4, x: 2, z: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, n: 5, t: 2}, what is the expected number of times the pattern 't+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 2, e: 1, i: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'e+n'? 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 4 letters from the multiset {j: 4, a: 5}. What is the expected number of occurrences of the pattern 'aj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 3, m: 2, e: 1, b: 2, d: 1}. What is the expected number of occurrences of the pattern 's+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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 4, y: 1, n: 2, p: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, e: 3, r: 3, a: 1}, what is the expected number of times the pattern 'rt+' 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 4 letters from the multiset {f: 2, c: 6, o: 1} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, j: 1, e: 3, y: 2} to form a word, what is the expected number of matches of the pattern 'j.*a'? 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 4 letters from the multiset {u: 4, c: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, l: 1, o: 3, r: 2}, what is the expected number of times the pattern 'ol+' 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 4 letters from the multiset {f: 3, p: 1, i: 1, e: 2, v: 2} 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, t: 2, e: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'ae*'? 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": "When randomly selecting 4 letters from the multiset {n: 6, y: 3} 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": "2.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, s: 1, o: 1, z: 4, t: 1}, 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": "0.49", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 1, n: 1, l: 1, q: 5, g: 1} to form a word, what is the expected number of matches of the pattern 'nl+'? 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 4 by randomly selecting letters from the multiset {g: 2, j: 2, h: 1, q: 2, n: 2}, what is the expected number of times the pattern 'jn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 2, j: 1, o: 2, i: 3, y: 1}, what is the expected number of times the pattern 'fi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, h: 2, u: 2, t: 2} to form a word, what is the expected number of matches of the pattern 't.*a'? Round 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 4 letters from the multiset {h: 3, m: 3, l: 1, v: 2} 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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 5, c: 4}, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, a: 1, k: 1, i: 2, j: 4}, what is the expected number of times the pattern 'jk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 4, e: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 3, p: 3, s: 1, y: 1, o: 1}. What is the expected number of occurrences of the pattern 'yp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, q: 2, h: 2, r: 2}. What is the expected number of occurrences of the pattern 'uh*' 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 4 letters from the multiset {m: 5, e: 3, i: 1}. What is the expected number of occurrences of the pattern 'i+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": "0.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 3, m: 1, w: 3, p: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, v: 1, c: 5, g: 2}. What is the expected number of occurrences of the pattern 'vg*' 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": "When randomly selecting 4 letters from the multiset {v: 3, x: 3, n: 1, z: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'n.*z'? 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 4 letters from the multiset {n: 5, w: 4} to form a word, what is the expected number of matches of the pattern 'w.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 1, u: 1, v: 2, t: 4, g: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 5, g: 4}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 1, b: 1, e: 2, x: 1, g: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 1, m: 2, v: 2, u: 2, k: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 1, h: 1, x: 3, c: 2, e: 2}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 2, d: 1, r: 3, v: 2, f: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 1, g: 3, s: 2, f: 3}, what is the expected number of times the pattern 'gf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, y: 3, z: 1, o: 3}, what is the expected number of times the pattern 'c+y' 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 4 letters from the multiset {f: 2, q: 3, c: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'q*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 3, k: 1, c: 1, u: 1, t: 3}. What is the expected number of occurrences of the pattern 'tc+' 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 4 letters from the multiset {e: 2, i: 2, d: 3, r: 2}. 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": "Form a word by randomly choosing 4 letters from the multiset {c: 3, u: 6}. What is the expected number of occurrences of the pattern 'uc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 4, y: 5} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 4, d: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 5, s: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 1, m: 3, c: 2, y: 1, s: 2}. 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, t: 1, d: 1, u: 3, p: 2}, what is the expected number of times the pattern 'p+u' 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 4 by randomly selecting letters from the multiset {w: 1, k: 1, p: 1, g: 1, m: 5}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, c: 2, e: 2, o: 1, s: 1}. What is the expected number of occurrences of the pattern 'x.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, e: 6, v: 1}. What is the expected number of occurrences of the pattern 'o*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": "3.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, w: 2, e: 4}, what is the expected number of times the pattern 'ew+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, z: 1, o: 1, a: 2, e: 3}, 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, i: 1, x: 5} to form a word, what is the expected number of matches of the pattern 'a+i'? 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 4 letters from the multiset {u: 3, b: 3, p: 1, i: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, u: 6}. 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": "2.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 3, a: 2, u: 1, b: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 7, q: 2} to form a word, what is the expected number of matches of the pattern 'a*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 7, w: 2}. 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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 5, s: 4}, what is the expected number of times the pattern 'h+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, w: 4, s: 4}. What is the expected number of occurrences of the pattern 'o.*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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 2, c: 2, y: 1, o: 4} to form a word, what is the expected number of matches of the pattern 'l+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 4, w: 3, 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, m: 4, d: 1, q: 1}. What is the expected number of occurrences of the pattern 't+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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, k: 2, w: 3, d: 2}, what is the expected number of times the pattern 'd*r' 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 4 letters from the multiset {h: 4, j: 5} 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 2, a: 1, m: 2, p: 1, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 2, w: 3, i: 1, y: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, g: 3, m: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 4, w: 1, j: 1, t: 2, u: 1}, what is the expected number of times the pattern 'j*t' 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 4 letters from the multiset {q: 1, o: 3, y: 4, e: 1} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 2, v: 3, c: 2, b: 1, u: 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": "0.54", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, o: 3, k: 2, f: 2, c: 1}. 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": "0.54", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 1, e: 1, i: 1, p: 3, v: 3} to form a word, what is the expected number of matches of the pattern 've+'? 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 4 letters from the multiset {k: 5, j: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, t: 3, a: 3, q: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, s: 2, h: 2, l: 4}. 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 2, v: 7}. What is the expected number of occurrences of the pattern 'e*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": "3.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 2, y: 3, e: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'y.*f'? Round 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 4 letters from the multiset {m: 1, l: 4, i: 2, t: 2}. What is the expected number of occurrences of the pattern 'lm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 1, p: 2, c: 2, b: 4}. 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": "Form a word by randomly choosing 4 letters from the multiset {m: 1, i: 3, h: 1, n: 2, r: 2}. 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 3, n: 3, o: 2, c: 1} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 2, g: 4, n: 3} to form a word, what is the expected number of matches of the pattern 'n*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.38", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 3, c: 3, i: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'ix*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 1, a: 2, f: 1, m: 3, b: 2} 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, u: 3, a: 3}, what is the expected number of times the pattern 'u*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, k: 3, c: 1, e: 2, b: 1}, what is the expected number of times the pattern 'ce+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 5, z: 4}, what is the expected number of times the pattern 'zd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 1, j: 1, a: 3, o: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'gg+'? 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 4 letters from the multiset {b: 1, y: 1, v: 2, k: 3, n: 2}. What is the expected number of occurrences of the pattern 'v.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 3, p: 1, o: 2, e: 3}. What is the expected number of occurrences of the pattern 'e+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": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 6, f: 3}, what is the expected number of times the pattern 'wf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 3, q: 2, p: 1, v: 3}. What is the expected number of occurrences of the pattern 'qv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, o: 3, a: 1, j: 3} 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": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, a: 5, t: 2}. What is the expected number of occurrences of the pattern 't+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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 2, u: 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 3, m: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'ma*'? 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 4 letters from the multiset {g: 4, t: 2, u: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 3, z: 1, r: 3, j: 1, e: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 1, l: 1, w: 1, m: 3, a: 3}, what is the expected number of times the pattern 'am+' 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 4 letters from the multiset {k: 4, q: 5}. 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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, v: 2, m: 4}, what is the expected number of times the pattern 'vm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, v: 3, r: 3}. What is the expected number of occurrences of the pattern 'r.*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": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 2, y: 1, h: 3, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, k: 1, w: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'k*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 5, e: 4}. What is the expected number of occurrences of the pattern 'o*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": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, t: 3, x: 1, k: 4}, what is the expected number of times the pattern 'g+t' 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 4 letters from the multiset {v: 3, d: 2, t: 4} to form a word, what is the expected number of matches of the pattern 'd*v'? 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 4 letters from the multiset {y: 1, c: 2, w: 4, t: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, u: 4, d: 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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 3, g: 2, f: 1, q: 2, w: 1} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 7, v: 2}. What is the expected number of occurrences of the pattern 'mv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 5, q: 3, f: 1}, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, a: 3, u: 2, i: 2} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 6, a: 3}. What is the expected number of occurrences of the pattern 'u+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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 3, j: 4, r: 2}, what is the expected number of times the pattern 'jg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 1, q: 2, y: 1, e: 3, x: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, d: 5}. What is the expected number of occurrences of the pattern 'dq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 6, f: 3}, what is the expected number of times the pattern 'f.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, e: 3, x: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'yx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, f: 1, y: 3, x: 2, v: 1}, 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": "When randomly selecting 4 letters from the multiset {w: 1, s: 2, b: 2, v: 4} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 7, o: 2}, what is the expected number of times the pattern 'j.*o' 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": "When randomly selecting 4 letters from the multiset {c: 1, h: 1, q: 1, d: 3, f: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, x: 6}, what is the expected number of times the pattern 'w+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 2, b: 1, m: 2, k: 2, j: 2} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 2, k: 4, l: 2, r: 1}. What is the expected number of occurrences of the pattern 'r*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": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 1, h: 3, w: 5} to form a word, what is the expected number of matches of the pattern 'we+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, m: 7}. What is the expected number of occurrences of the pattern 'm*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": "1.94", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 1, h: 1, w: 2, o: 3, g: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 6, e: 3}, what is the expected number of times the pattern 'e*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 8, g: 1}, what is the expected number of times the pattern 'sg+' 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": "When randomly selecting 4 letters from the multiset {q: 3, b: 2, l: 2, f: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'q+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 6, d: 3} 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": "3.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 6, f: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 1, p: 3, q: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'y+p'? 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 4 letters from the multiset {i: 3, x: 3, r: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 5, f: 4} 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": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 2, f: 3, t: 4}. What is the expected number of occurrences of the pattern 'tp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 5, v: 4}, what is the expected number of times the pattern 'hv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, f: 2, g: 3} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, s: 2, c: 4}, what is the expected number of times the pattern 'c+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 4, g: 2, i: 3}. 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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 3, r: 2, n: 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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, g: 5}. 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 1, u: 2, d: 3, k: 3}, what is the expected number of times the pattern 'd.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 6, f: 3} to form a word, what is the expected number of matches of the pattern 'f.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, r: 3, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 5, s: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, s: 2, l: 2, r: 2}. What is the expected number of occurrences of the pattern 'l+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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 1, p: 1, r: 1, z: 4, u: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 1, f: 2, b: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'mg+'? 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 4 letters from the multiset {m: 3, e: 2, s: 1, x: 1, j: 2}. What is the expected number of occurrences of the pattern 'sx+' 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 4 letters from the multiset {c: 4, r: 5} to form a word, what is the expected number of matches of the pattern 'cr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, y: 3, x: 4, v: 1}. What is the expected number of occurrences of the pattern 'yr+' 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 4 letters from the multiset {y: 2, c: 5, w: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, i: 3, w: 3, l: 1}, what is the expected number of times the pattern 'lw+' appears? 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": "Form a word by randomly choosing 4 letters from the multiset {k: 4, y: 5}. 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 2, c: 2, a: 2, m: 2, q: 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 4, a: 5}. What is the expected number of occurrences of the pattern 'i+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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 5, j: 4}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 1, j: 2, d: 2, z: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'd*q'? 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 4 letters from the multiset {u: 1, s: 1, n: 4, y: 1, k: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, k: 2, p: 1, f: 4}, what is the expected number of times the pattern 'k+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 2, z: 2, t: 2, w: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 1, m: 2, n: 3, o: 1, u: 2} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 4, y: 5} to form a word, what is the expected number of matches of the pattern 'y*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, f: 5}, what is the expected number of times the pattern 'd*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, g: 4, h: 3}, what is the expected number of times the pattern 'g.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 5, e: 4} 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 6, o: 3}, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 3, t: 3, a: 3} to form a word, what is the expected number of matches of the pattern 't.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, l: 1, w: 2, n: 3}. What is the expected number of occurrences of the pattern 'lw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 4, l: 3, q: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, o: 3, m: 1, g: 2} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, o: 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": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 2, b: 2, r: 3, l: 2}. 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, s: 3, g: 1, u: 2, r: 1}, what is the expected number of times the pattern 'g.*g' 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 4 by randomly selecting letters from the multiset {a: 4, h: 5}, what is the expected number of times the pattern 'h.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, a: 5}, what is the expected number of times the pattern 'a+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 2, h: 3, j: 2, q: 2} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 1, i: 1, h: 3, c: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'ic*'? 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 4 letters from the multiset {y: 1, s: 1, v: 3, i: 2, f: 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, v: 2, i: 2, h: 4}. What is the expected number of occurrences of the pattern 'v.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 3, i: 2, w: 1, c: 1, t: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 4, k: 5}, what is the expected number of times the pattern 'k*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, o: 3, u: 4}. What is the expected number of occurrences of the pattern 'uc*' 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 4 letters from the multiset {v: 1, n: 6, c: 2} to form a word, what is the expected number of matches of the pattern 'v*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.92", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 7, o: 2}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 5, y: 4}. What is the expected number of occurrences of the pattern 'yy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 4, x: 2, t: 3}. What is the expected number of occurrences of the pattern 'gt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 4, y: 2, p: 3}. What is the expected number of occurrences of the pattern 'ys*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 2, o: 4, u: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 5, e: 4}, what is the expected number of times the pattern 'ue+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 5, y: 4}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 1, f: 2, b: 2, e: 1, o: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 2, x: 2, i: 3, y: 1, z: 1}, 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": "1.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, n: 3, c: 3}, what is the expected number of times the pattern 'nc*' appears? Round 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 4 letters from the multiset {e: 5, b: 4}. What is the expected number of occurrences of the pattern 'ee+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, p: 4, n: 1, r: 1, d: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, y: 2, m: 3, u: 2}, what is the expected number of times the pattern 'm.*y' appears? Round 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 4 letters from the multiset {c: 3, p: 3, y: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'p.*y'? Round 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 4 letters from the multiset {n: 3, s: 5, u: 1}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, x: 3, v: 3, a: 1} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 4, q: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, i: 4, v: 2, e: 1}, what is the expected number of times the pattern 'r.*i' appears? 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": "Form a word by randomly choosing 4 letters from the multiset {k: 3, i: 1, e: 2, y: 2, u: 1}. What is the expected number of occurrences of the pattern 'u+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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 4, u: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'ua*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 2, p: 1, x: 3, m: 1, f: 2}. What is the expected number of occurrences of the pattern 'xm+' 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 4 by randomly selecting letters from the multiset {j: 1, t: 3, w: 5}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 2, g: 5, o: 2} to form a word, what is the expected number of matches of the pattern 'gs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 1, i: 4, r: 4} to form a word, what is the expected number of matches of the pattern 'i+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.89", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, y: 2, j: 2, v: 2}. 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 4, v: 5} to form a word, what is the expected number of matches of the pattern 'v*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 4, m: 5} 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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 5, e: 4}. What is the expected number of occurrences of the pattern 'x*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": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 2, s: 2, f: 2, c: 3}. What is the expected number of occurrences of the pattern 's*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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 4, o: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, m: 5}. What is the expected number of occurrences of the pattern 'xm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, j: 1, l: 4, r: 2}, what is the expected number of times the pattern 'dj+' 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 4 letters from the multiset {b: 1, d: 3, z: 5} 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, f: 5}. What is the expected number of occurrences of the pattern 'f+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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 5, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 5, e: 2, o: 2} 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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 4, h: 5}. What is the expected number of occurrences of the pattern 'v*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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, n: 4, v: 1, g: 2}, what is the expected number of times the pattern 'v+g' 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 4 letters from the multiset {p: 5, v: 4} to form a word, what is the expected number of matches of the pattern 'p.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 5, t: 2, j: 2}, 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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 6, v: 3} to form a word, what is the expected number of matches of the pattern 'z.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, o: 2, i: 1, a: 2, v: 1}. What is the expected number of occurrences of the pattern 'o.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, l: 1, j: 1, k: 3, g: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, o: 1, v: 4, j: 1, c: 1}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, e: 1, t: 3, j: 2, m: 2}, what is the expected number of times the pattern 'g.*g' 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 4 letters from the multiset {c: 3, i: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 4, q: 4, y: 1}. What is the expected number of occurrences of the pattern 'y*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": "1.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, s: 3, t: 3}, 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": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 5, i: 4}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, l: 2, m: 3, s: 2}, what is the expected number of times the pattern 's.*l' 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": "When randomly selecting 4 letters from the multiset {q: 4, d: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'd.*j'? Round 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 4 letters from the multiset {a: 3, v: 2, g: 3, s: 1}. What is the expected number of occurrences of the pattern 'g*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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 1, f: 8}. What is the expected number of occurrences of the pattern 'p*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": "3.89", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, q: 4, k: 1, n: 2}. What is the expected number of occurrences of the pattern 'd.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, m: 3, w: 3}. What is the expected number of occurrences of the pattern 'w*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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 1, j: 2, z: 2, o: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'dj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 2, t: 2, h: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 3, m: 1, t: 2, n: 3}. What is the expected number of occurrences of the pattern 'nm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 2, j: 1, s: 2, h: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'g+h'? 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 4 by randomly selecting letters from the multiset {j: 3, s: 2, i: 4}, what is the expected number of times the pattern 'js+' 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 4 letters from the multiset {d: 4, y: 1, l: 4}. What is the expected number of occurrences of the pattern 'y.*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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 1, f: 3, p: 1, g: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'n.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, a: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 3, g: 2, y: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, b: 2, n: 1, h: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'vn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 5, y: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 4, a: 5}. What is the expected number of occurrences of the pattern 'a+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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 1, i: 3, z: 1, l: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'l+v'? 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": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, l: 3, c: 1, x: 1, q: 2}, what is the expected number of times the pattern 's*l' 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 4 letters from the multiset {x: 4, k: 5}. What is the expected number of occurrences of the pattern 'xk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, c: 2, p: 2, v: 2}, what is the expected number of times the pattern 'c+y' 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 4 letters from the multiset {w: 3, c: 2, n: 3, o: 1}. What is the expected number of occurrences of the pattern 'c.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, p: 2, s: 2, i: 1, t: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 2, y: 3, i: 4} to form a word, what is the expected number of matches of the pattern 'x*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": "When randomly selecting 4 letters from the multiset {l: 1, i: 1, p: 6, s: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, m: 2, d: 2, z: 2}. 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": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, d: 3, u: 1, k: 2}. 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": "0.97", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, d: 4, k: 1, o: 1, j: 2}, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 2, t: 1, n: 2, v: 2, q: 2} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, g: 1, f: 2, p: 1, d: 3}, what is the expected number of times the pattern 'g.*g' 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 4 letters from the multiset {u: 2, h: 7} 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": "3.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 1, s: 1, v: 2, n: 2, a: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 6, y: 3}. What is the expected number of occurrences of the pattern 'yd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 4, i: 5}, what is the expected number of times the pattern 'i+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, k: 2, z: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, s: 3, i: 4}. What is the expected number of occurrences of the pattern 'u+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": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 3, t: 2, q: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'n*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 3, x: 2, k: 1, s: 3}. What is the expected number of occurrences of the pattern 'n+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": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, o: 4, d: 2}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 4, p: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'sp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, x: 6} to form a word, what is the expected number of matches of the pattern 'xd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 5, n: 4}, what is the expected number of times the pattern 'jn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 5, r: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 1, a: 3, s: 2, x: 2, n: 1}. 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, p: 1, w: 1, a: 5}, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, q: 3, k: 3}, what is the expected number of times the pattern 'q*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, t: 6} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 4, f: 2, m: 1, g: 2}. What is the expected number of occurrences of the pattern 'g+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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 4, p: 1, u: 4}, what is the expected number of times the pattern 'i*p' appears? 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 4 by randomly selecting letters from the multiset {y: 3, a: 2, x: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, t: 1, c: 4}. What is the expected number of occurrences of the pattern 'q*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": "2.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, k: 2, e: 2, i: 3, o: 1}, what is the expected number of times the pattern 'mi+' appears? 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": "Form a word by randomly choosing 4 letters from the multiset {k: 1, i: 3, z: 2, m: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 2, m: 1, q: 2, f: 4} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, c: 6}. What is the expected number of occurrences of the pattern 'p.*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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 1, c: 2, o: 2, d: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'ot+'? 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 4 letters from the multiset {f: 7, p: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 4, g: 5}. What is the expected number of occurrences of the pattern 's.*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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 1, l: 1, u: 2, r: 3, w: 2}, what is the expected number of times the pattern 'w*u' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, h: 2, w: 1, o: 1, g: 3}, what is the expected number of times the pattern 'ow*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 2, y: 2, b: 3, a: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 6, f: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, e: 2, p: 2, i: 2}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, m: 3, f: 2, z: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, x: 3, m: 4}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 3, m: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'y*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 4, y: 2, i: 3}. What is the expected number of occurrences of the pattern 'y.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 5, d: 1, r: 3}, what is the expected number of times the pattern 'z*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 5, d: 4} to form a word, what is the expected number of matches of the pattern 'k*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 4, e: 2, f: 1, o: 1, g: 1}, what is the expected number of times the pattern 'eo+' 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 4 letters from the multiset {j: 1, i: 2, r: 2, l: 3, o: 1}. What is the expected number of occurrences of the pattern 'l*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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 4, d: 3, e: 1, v: 1}. What is the expected number of occurrences of the pattern 'v*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": "1.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 2, b: 2, x: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'x.*b'? Round 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 4 letters from the multiset {y: 3, d: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'y.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 3, a: 4, i: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 2, d: 3, i: 2, x: 2}. What is the expected number of occurrences of the pattern 'd.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 1, o: 3, p: 2, k: 2, x: 1}, what is the expected number of times the pattern 'x.*u' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, q: 2, h: 2, l: 2, w: 1}, what is the expected number of times the pattern 'qw+' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 1, z: 3, m: 3, e: 2}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 1, c: 1, h: 2, a: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, d: 1, i: 1, a: 4, o: 2}, what is the expected number of times the pattern 'id+' appears? 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": "When randomly selecting 4 letters from the multiset {f: 3, y: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'y*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 3, i: 5, a: 1} 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 5, h: 4} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 3, h: 2, f: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'fq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 3, r: 1, b: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'pb*'? 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 4 letters from the multiset {k: 1, y: 1, h: 2, u: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, c: 3, z: 5}, what is the expected number of times the pattern 'zc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 5, y: 4} 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, c: 5}. What is the expected number of occurrences of the pattern 'c.*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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 7, 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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 5, b: 4} 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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 4, k: 1, q: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'i+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 3, i: 3, u: 3}. What is the expected number of occurrences of the pattern 'iu+' 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 4 letters from the multiset {z: 2, n: 7} to form a word, what is the expected number of matches of the pattern 'z+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 4, p: 3, t: 2}, what is the expected number of times the pattern 'p*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 3, w: 3, e: 3}. What is the expected number of occurrences of the pattern 'e.*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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 2, j: 2, q: 1, c: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'oc+'? 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 4 letters from the multiset {p: 5, e: 4} to form a word, what is the expected number of matches of the pattern 'e*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 4, y: 1, v: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 2, y: 1, p: 3, d: 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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 1, j: 2, o: 2, f: 1, n: 3}, what is the expected number of times the pattern 'f*j' 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 4 by randomly selecting letters from the multiset {w: 5, b: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, y: 1, q: 3, m: 1, j: 2}. What is the expected number of occurrences of the pattern 'm*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": "0.97", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, g: 1, m: 6}, what is the expected number of times the pattern 'g+m' 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 4 by randomly selecting letters from the multiset {s: 1, a: 2, n: 1, v: 2, y: 3}, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 6, o: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, w: 3, e: 4}, what is the expected number of times the pattern 'ew+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, v: 2, k: 1, p: 1, x: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, q: 3, b: 5}, 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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, h: 6} to form a word, what is the expected number of matches of the pattern 'hw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, x: 3, k: 2, b: 2}. 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 5, t: 4}. What is the expected number of occurrences of the pattern 'z+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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, s: 4, k: 2}. What is the expected number of occurrences of the pattern 'ks*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, i: 3, k: 2}. What is the expected number of occurrences of the pattern 'i+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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, t: 2, d: 3, v: 1}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, m: 3, x: 2, d: 2, n: 1}, what is the expected number of times the pattern 'xz*' 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 4 by randomly selecting letters from the multiset {r: 3, j: 2, c: 2, z: 2}, what is the expected number of times the pattern 'j*r' 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 4 by randomly selecting letters from the multiset {q: 4, t: 5}, what is the expected number of times the pattern 't*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 3, w: 3, h: 2, a: 1} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, h: 3, a: 2}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 5, f: 2, w: 1, g: 1}. What is the expected number of occurrences of the pattern 'v+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": "0.31", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 6, l: 3} to form a word, what is the expected number of matches of the pattern 'm+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 4, y: 3, z: 2}. 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": "2.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, n: 5}, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 2, d: 5, v: 2}, what is the expected number of times the pattern 'ov*' 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 4 letters from the multiset {x: 5, r: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, p: 1, q: 6}. What is the expected number of occurrences of the pattern 'o+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": "0.55", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 2, v: 2, x: 2, d: 2, b: 1}. What is the expected number of occurrences of the pattern 'xb+' 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 4 by randomly selecting letters from the multiset {d: 4, v: 5}, what is the expected number of times the pattern 'd*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, o: 3, p: 4} to form a word, what is the expected number of matches of the pattern 'm+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 3, r: 4, w: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 5, m: 4} to form a word, what is the expected number of matches of the pattern 'm*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, m: 1, f: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'fm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, l: 3, c: 4}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, q: 3, d: 2}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 3, j: 2, w: 2, x: 1, r: 1} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, w: 3, k: 2, z: 2}, what is the expected number of times the pattern 'k*w' 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": "When randomly selecting 4 letters from the multiset {h: 6, w: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, g: 5, x: 2} to form a word, what is the expected number of matches of the pattern 'x*y'? 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 4 letters from the multiset {t: 1, q: 2, e: 2, g: 3, p: 1} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 2, g: 2, n: 2, l: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, e: 5, i: 1}, what is the expected number of times the pattern 'ez*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 4, b: 1, f: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'f+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 5, y: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 2, i: 1, u: 3, k: 1, x: 2}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, q: 1, e: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, l: 4, n: 3}. What is the expected number of occurrences of the pattern 'x+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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, r: 1, a: 5, p: 1}, what is the expected number of times the pattern 'p*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 6, k: 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, v: 2, t: 3, w: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 6, u: 3} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 2, c: 4, v: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'f+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, d: 1, s: 4, e: 2}. What is the expected number of occurrences of the pattern 'e+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": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, l: 2, z: 1, n: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 2, u: 3, o: 4} 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": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 7, b: 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, q: 2, s: 1, o: 3}, what is the expected number of times the pattern 'q*o' 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": "When randomly selecting 4 letters from the multiset {z: 1, i: 1, r: 2, g: 5} to form a word, what is the expected number of matches of the pattern 'i*r'? 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 4 letters from the multiset {d: 3, x: 1, m: 2, v: 2, h: 1}. What is the expected number of occurrences of the pattern 'v.*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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 3, s: 2, k: 4}, what is the expected number of times the pattern 'hk+' appears? 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": "Form a word by randomly choosing 4 letters from the multiset {h: 2, a: 2, i: 1, q: 2, o: 2}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 5, a: 3, j: 1}, what is the expected number of times the pattern 'q.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 2, e: 2, c: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 2, a: 2, u: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'ca+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, a: 5}, what is the expected number of times the pattern 'va*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 6, y: 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 2, l: 7} to form a word, what is the expected number of matches of the pattern 'lh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, z: 3, a: 2}. 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 2, c: 1, s: 3, n: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 3, s: 3, h: 1, m: 1, f: 1} 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, u: 2, q: 5}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 3, e: 2, m: 2, i: 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 3, g: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'yg*'? 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 4 letters from the multiset {t: 3, d: 1, u: 1, c: 3, n: 1}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, i: 2, z: 4, m: 1}, 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": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 6, y: 3}, what is the expected number of times the pattern 'yl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 6, i: 3}, what is the expected number of times the pattern 'hi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 2, q: 1, a: 2, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 4, t: 5}. What is the expected number of occurrences of the pattern 'tl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 1, m: 3, c: 2, f: 2, i: 1}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 3, d: 3, m: 3}. What is the expected number of occurrences of the pattern 'c.*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": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, f: 2, s: 2, u: 1, o: 2}, what is the expected number of times the pattern 'l+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 1, m: 2, p: 2, l: 2, s: 2}, what is the expected number of times the pattern 'hs*' 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 4 by randomly selecting letters from the multiset {n: 2, m: 2, j: 3, g: 2}, what is the expected number of times the pattern 'n+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 4, o: 2, y: 3}. What is the expected number of occurrences of the pattern 'y+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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, s: 4}. What is the expected number of occurrences of the pattern 'sl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 4, e: 5}, what is the expected number of times the pattern 'we*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 3, f: 2, j: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'c+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, z: 3, d: 3, s: 2}. What is the expected number of occurrences of the pattern 'sd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 6, h: 3}, what is the expected number of times the pattern 'eh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, u: 3, t: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 1, v: 2, e: 2, i: 1, u: 3} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 2, h: 2, b: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'z.*b'? 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 4 by randomly selecting letters from the multiset {n: 2, f: 2, b: 2, u: 3}, what is the expected number of times the pattern 'u*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 5, c: 4} to form a word, what is the expected number of matches of the pattern 'u.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 2, n: 3, b: 4}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 4, f: 5} to form a word, what is the expected number of matches of the pattern 'f*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, t: 3, g: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'tz+'? 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 4 letters from the multiset {i: 3, k: 3, j: 1, s: 2}. What is the expected number of occurrences of the pattern 's*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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 5, c: 2, m: 2}. 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 3, m: 2, h: 1, k: 3}. What is the expected number of occurrences of the pattern 'm*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": "1.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 1, h: 3, p: 5} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 3, e: 4, z: 2}. What is the expected number of occurrences of the pattern 'e*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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 7, m: 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 3, w: 2, i: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'u*i'? 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": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 6, m: 3}, what is the expected number of times the pattern 'ma*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 3, b: 2, m: 2, j: 1, n: 1} to form a word, what is the expected number of matches of the pattern 's+n'? 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 4 letters from the multiset {g: 3, a: 3, h: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'a+g'? 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": "When randomly selecting 4 letters from the multiset {m: 2, i: 2, r: 1, d: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'm*r'? 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": "Form a word by randomly choosing 4 letters from the multiset {c: 3, h: 3, s: 3}. 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 4, l: 5}, what is the expected number of times the pattern 'wl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, z: 1, i: 4, u: 2}, what is the expected number of times the pattern 'i*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 4, y: 2, o: 3}, what is the expected number of times the pattern 'yh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 1, p: 3, s: 2, t: 2, o: 1}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 5, y: 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 5, c: 4} 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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 5, g: 4} 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, s: 1, b: 2, j: 1, k: 1}, what is the expected number of times the pattern 'k+j' appears? 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 4 by randomly selecting letters from the multiset {q: 3, d: 6}, what is the expected number of times the pattern 'd*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 2, w: 3, m: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'w+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}