{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 6, d: 4}. 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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 3, r: 1, b: 3, z: 1, d: 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": "0.66", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 4, r: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'rp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 3, x: 2, c: 4, b: 1} to form a word, what is the expected number of matches of the pattern 'q+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, j: 5, x: 2, f: 2}. What is the expected number of occurrences of the pattern 'f+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 6, w: 4}, what is the expected number of times the pattern 'wc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, i: 1, h: 1, d: 3, o: 2}, what is the expected number of times the pattern 'o.*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 5 by randomly selecting letters from the multiset {e: 3, h: 2, r: 1, z: 4}, what is the expected number of times the pattern 'rh*' 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 5 letters from the multiset {d: 1, f: 2, p: 2, h: 2, e: 3} 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 3, j: 4, h: 3}, 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": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 2, g: 2, h: 2, o: 4}. What is the expected number of occurrences of the pattern 'oh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 1, x: 1, w: 2, s: 1, c: 5} to form a word, what is the expected number of matches of the pattern 'xr+'? 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 5 letters from the multiset {x: 2, t: 3, m: 1, h: 4} to form a word, what is the expected number of matches of the pattern 't+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 2, x: 3, v: 2, j: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'gf+'? 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 5 letters from the multiset {r: 4, a: 6} to form a word, what is the expected number of matches of the pattern 'a.*r'? 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": "When randomly selecting 5 letters from the multiset {l: 3, o: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'j+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 3, x: 4, m: 3} to form a word, what is the expected number of matches of the pattern 'a*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 2, x: 3, p: 2, n: 2, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 2, v: 1, s: 2, t: 2, c: 3}, 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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 2, b: 1, l: 2, m: 1, i: 4}, 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 2, w: 4, z: 2, e: 1, i: 1}. What is the expected number of occurrences of the pattern 'w.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.89", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 5, r: 4, c: 1}, what is the expected number of times the pattern 'l*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 4, r: 3, j: 3}, what is the expected number of times the pattern 'e.*j' 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 5 by randomly selecting letters from the multiset {t: 3, s: 3, f: 4}, what is the expected number of times the pattern 'f.*s' 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": "Form a word by randomly choosing 5 letters from the multiset {e: 2, j: 3, k: 2, p: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 2, z: 3, d: 3, o: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 1, y: 1, l: 2, v: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'rv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 1, h: 3, t: 2, n: 2, i: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 1, y: 1, e: 2, u: 2, l: 4}, what is the expected number of times the pattern 'eu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, c: 2, z: 2, f: 3, x: 1}. What is the expected number of occurrences of the pattern 'fz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 3, n: 3, e: 4} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 1, o: 5, h: 4} to form a word, what is the expected number of matches of the pattern 'p.*h'? 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 5 by randomly selecting letters from the multiset {w: 1, y: 2, b: 2, d: 4, q: 1}, what is the expected number of times the pattern 'dd+' 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 5 letters from the multiset {i: 4, t: 6} to form a word, what is the expected number of matches of the pattern 't+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 1, m: 2, j: 1, o: 5, g: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 4, f: 3, w: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'y+w'? 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 5 by randomly selecting letters from the multiset {k: 5, m: 5}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 2, e: 3, q: 1, f: 4} 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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, i: 2, k: 2, l: 2}, what is the expected number of times the pattern 'k+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 5, o: 1, t: 3, w: 1}, what is the expected number of times the pattern 'te*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 1, p: 4, o: 3, w: 2}. What is the expected number of occurrences of the pattern 'w+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": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, j: 3, u: 3}. 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": "2.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, h: 2, n: 2, b: 1, t: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, n: 2, g: 5}, 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 6, i: 4}. What is the expected number of occurrences of the pattern 'ip*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 5, s: 2, x: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, y: 3, v: 1, f: 2, t: 2}. What is the expected number of occurrences of the pattern 'f+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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 7, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 6, m: 4} to form a word, what is the expected number of matches of the pattern 'mi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 1, i: 3, e: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, c: 7}. What is the expected number of occurrences of the pattern 'c+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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 3, e: 2, l: 2, u: 1, b: 2} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 3, t: 3, p: 1, i: 1, o: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 5, n: 5}. What is the expected number of occurrences of the pattern 'p.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 2, s: 1, i: 2, u: 4, y: 1} 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": "0.54", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 5, o: 2, b: 2, c: 1}. What is the expected number of occurrences of the pattern 'ob*' 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 5 letters from the multiset {q: 1, r: 3, g: 1, t: 1, v: 4}. What is the expected number of occurrences of the pattern 'g.*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": "0.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 1, n: 2, c: 1, a: 1, h: 5}. What is the expected number of occurrences of the pattern 'n.*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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 5, y: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'yl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 2, c: 2, w: 2, s: 1, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 2, n: 4, t: 2, x: 2}. What is the expected number of occurrences of the pattern 'x+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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 2, l: 8} to form a word, what is the expected number of matches of the pattern 'l+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, t: 2, n: 3, e: 2, p: 1}. 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 1, t: 3, k: 2, o: 1, b: 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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 2, u: 1, o: 1, q: 2, y: 4}, what is the expected number of times the pattern 'q.*u' 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 5 by randomly selecting letters from the multiset {y: 1, j: 3, w: 2, b: 3, d: 1}, 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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 5, b: 3, u: 2}. 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 3, b: 3, y: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 3, x: 6, c: 1}. 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": "3.96", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, b: 2, o: 3, x: 3}, what is the expected number of times the pattern 'co*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 4, g: 2, m: 2, k: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 6, m: 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 2, z: 1, s: 1, q: 3, g: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 6, x: 4}, what is the expected number of times the pattern 'x.*e' appears? 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": "When randomly selecting 5 letters from the multiset {b: 3, q: 2, f: 2, u: 3} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 2, h: 3, x: 3, c: 2}, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 2, h: 3, u: 1, p: 4} to form a word, what is the expected number of matches of the pattern 'i*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 4, g: 2, o: 2, n: 2}, what is the expected number of times the pattern 'g+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, w: 1, q: 3, j: 4}, what is the expected number of times the pattern 'jw+' 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 5 letters from the multiset {h: 1, g: 4, i: 5}. What is the expected number of occurrences of the pattern 'i+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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 5, s: 3, z: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 2, z: 3, e: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'es*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, k: 3, v: 4}, what is the expected number of times the pattern 'm*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 1, g: 1, q: 3, w: 4, e: 1}, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 3, z: 3, i: 4} to form a word, what is the expected number of matches of the pattern 'k.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 7, w: 3} to form a word, what is the expected number of matches of the pattern 'w.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 2, s: 3, d: 5} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 4, s: 1, k: 3, e: 2}. What is the expected number of occurrences of the pattern 's*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, l: 3, p: 2, g: 3}, what is the expected number of times the pattern 'lg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 5, a: 4, k: 1}. What is the expected number of occurrences of the pattern 'n*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": "When randomly selecting 5 letters from the multiset {d: 1, j: 9} to form a word, what is the expected number of matches of the pattern 'j*d'? 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 5 by randomly selecting letters from the multiset {t: 5, i: 5}, what is the expected number of times the pattern 'it*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 2, k: 1, c: 1, d: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'zk+'? 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 5 letters from the multiset {u: 2, j: 1, a: 3, x: 2, m: 2}. What is the expected number of occurrences of the pattern 'u.*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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 4, j: 1, l: 3, v: 1, d: 1}, what is the expected number of times the pattern 'lj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 4, d: 6} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, z: 1, v: 1, p: 4, a: 2}, what is the expected number of times the pattern 'sa*' 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 5 by randomly selecting letters from the multiset {a: 3, w: 1, s: 1, g: 3, b: 2}, 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": "1.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 2, h: 3, n: 5} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 3, q: 1, i: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 3, l: 3, q: 3, x: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 7, z: 3} to form a word, what is the expected number of matches of the pattern 'z+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 2, b: 1, l: 4, t: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r+q'? 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 5 letters from the multiset {u: 2, a: 2, d: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 2, j: 3, p: 1, i: 3, u: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 3, t: 7} 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": "4.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 1, d: 1, h: 3, p: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 1, y: 2, u: 3, z: 2, i: 2}. 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 1, l: 3, c: 3, v: 3}, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 3, i: 2, r: 2, c: 1, j: 2}. What is the expected number of occurrences of the pattern 'ir+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 4, j: 2, b: 4}, what is the expected number of times the pattern 'c*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 4, f: 3, k: 3}. 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 7, k: 3} to form a word, what is the expected number of matches of the pattern 'k+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 3, d: 3, w: 4} to form a word, what is the expected number of matches of the pattern 'dn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 5, j: 2, o: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 5, n: 5}, what is the expected number of times the pattern 'nw+' 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 5 letters from the multiset {l: 8, k: 2}. What is the expected number of occurrences of the pattern 'l*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 8, s: 2}, 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 4, k: 2, p: 2, f: 2}, what is the expected number of times the pattern 'wp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 2, l: 3, k: 2, h: 1, t: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, v: 5, n: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 3, j: 4, b: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 3, w: 3, g: 4} to form a word, what is the expected number of matches of the pattern 'g.*w'? 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 5 by randomly selecting letters from the multiset {f: 1, e: 3, u: 2, h: 3, l: 1}, what is the expected number of times the pattern 'u+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 3, l: 2, g: 1, q: 2, m: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, f: 1, k: 4, p: 1, g: 2}, 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, w: 3, f: 3, b: 2, z: 1}. What is the expected number of occurrences of the pattern 'z*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 2, l: 2, a: 4, j: 1, b: 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": "When randomly selecting 5 letters from the multiset {h: 1, r: 3, z: 3, k: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'k*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 3, f: 1, x: 4, v: 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": "Form a word by randomly choosing 5 letters from the multiset {j: 4, t: 6}. What is the expected number of occurrences of the pattern 't.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 4, s: 4, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 6, w: 4}. What is the expected number of occurrences of the pattern 'wf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 4, j: 6} to form a word, what is the expected number of matches of the pattern 'ju+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 3, z: 5, r: 2} to form a word, what is the expected number of matches of the pattern 'ry*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 2, g: 3, h: 1, i: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'fh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 2, p: 2, y: 2, s: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'sz*'? 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 5 letters from the multiset {p: 4, m: 2, t: 2, r: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 4, m: 1, a: 1, o: 3, z: 1}. What is the expected number of occurrences of the pattern 'oa+' in 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 5 letters from the multiset {n: 3, z: 1, f: 4, a: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'n+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 3, i: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'rl+'? 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 5 letters from the multiset {v: 4, y: 1, t: 1, r: 1, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 4, q: 6} 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": "4.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 2, w: 2, f: 2, u: 4}, what is the expected number of times the pattern 'yf*' 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": "Form a word by randomly choosing 5 letters from the multiset {u: 1, n: 1, j: 3, t: 3, q: 2}. What is the expected number of occurrences of the pattern 't.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 2, b: 2, e: 6}. What is the expected number of occurrences of the pattern 'e.*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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 1, m: 4, s: 2, f: 2, g: 1}, what is the expected number of times the pattern 'mf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, x: 4, l: 4}, what is the expected number of times the pattern 'xl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, u: 6}. What is the expected number of occurrences of the pattern 'f*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, e: 2, h: 2, u: 3, z: 1}, what is the expected number of times the pattern 'p+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 2, x: 4, l: 4}. What is the expected number of occurrences of the pattern 'x*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 4, b: 1, a: 3, o: 1, m: 1}, 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 5 by randomly selecting letters from the multiset {j: 5, z: 5}, what is the expected number of times the pattern 'jz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 4, m: 2, q: 4}. What is the expected number of occurrences of the pattern 'q*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 3, m: 5, z: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, q: 6}, what is the expected number of times the pattern 'qv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 2, r: 2, p: 2, m: 4} 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 2, h: 2, p: 6} to form a word, what is the expected number of matches of the pattern 'p+q'? 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 5 letters from the multiset {n: 3, u: 2, q: 1, j: 2, e: 2}. What is the expected number of occurrences of the pattern 'j.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 2, l: 3, v: 3, r: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 3, c: 4, i: 3} to form a word, what is the expected number of matches of the pattern 'i*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 2, k: 4, o: 2, b: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 1, e: 2, d: 3, y: 1, j: 3}. 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": "0.66", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 4, h: 2, y: 4}, what is the expected number of times the pattern 'yi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 4, c: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'qc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 2, p: 1, k: 5, g: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 4, n: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, u: 6}, what is the expected number of times the pattern 'v.*u' appears? 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": "When randomly selecting 5 letters from the multiset {d: 4, z: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'd+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 3, v: 4, e: 3}. 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 5, y: 3, o: 2}, what is the expected number of times the pattern 'o*y' 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 5 by randomly selecting letters from the multiset {k: 2, l: 1, v: 5, g: 2}, what is the expected number of times the pattern 'k*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.99", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 4, n: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*n'? 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 5 by randomly selecting letters from the multiset {g: 2, w: 1, j: 3, r: 4}, what is the expected number of times the pattern 'gj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 3, e: 4, i: 3}. What is the expected number of occurrences of the pattern 'e.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 1, w: 3, q: 2, l: 3, n: 1}, what is the expected number of times the pattern 'nw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 3, k: 7}. 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 2, v: 8}, what is the expected number of times the pattern 'v.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 5, n: 5}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 5, i: 5} to form a word, what is the expected number of matches of the pattern 's.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 4, d: 2, s: 1, v: 2, e: 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": "When randomly selecting 5 letters from the multiset {c: 4, p: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'p+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 8, e: 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": "6.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 2, p: 2, e: 6}, what is the expected number of times the pattern 'ey*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 2, n: 2, b: 3, s: 2, d: 1}. 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 3, w: 4, j: 3} 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": "0.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 2, u: 3, i: 3, o: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 4, q: 6}. What is the expected number of occurrences of the pattern 'x+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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 4, j: 6}, what is the expected number of times the pattern 'j+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 2, m: 1, e: 4, y: 3} to form a word, what is the expected number of matches of the pattern 'm*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 3, d: 2, n: 2, e: 2, t: 1}. What is the expected number of occurrences of the pattern 'en*' 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 5 letters from the multiset {g: 5, j: 5} to form a word, what is the expected number of matches of the pattern 'g*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 2, a: 4, j: 4} to form a word, what is the expected number of matches of the pattern 'jv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, h: 3, r: 3, o: 2}. What is the expected number of occurrences of the pattern 'rl*' 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 5 letters from the multiset {y: 3, d: 7}. 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 4, f: 6} 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, y: 1, d: 3, a: 2, c: 2}, what is the expected number of times the pattern 'a*y' 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 5 letters from the multiset {k: 6, w: 4} to form a word, what is the expected number of matches of the pattern 'k+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, o: 4, h: 3}, 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": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 1, w: 9} to form a word, what is the expected number of matches of the pattern 'd*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, m: 1, s: 2, v: 2, h: 2}, 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 3, c: 3, i: 4} to form a word, what is the expected number of matches of the pattern 'jc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 2, q: 2, f: 3, e: 2, v: 1}, what is the expected number of times the pattern 'v+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 5 by randomly selecting letters from the multiset {m: 7, x: 3}, what is the expected number of times the pattern 'xm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 1, j: 3, s: 2, m: 1, g: 3}, what is the expected number of times the pattern 'wj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, b: 3, g: 4}, what is the expected number of times the pattern 'g.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 4, f: 6} to form a word, what is the expected number of matches of the pattern 'f.*o'? 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": "When randomly selecting 5 letters from the multiset {c: 3, n: 4, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 5, x: 5}. 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, a: 6, v: 1}, what is the expected number of times the pattern 'xv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 3, d: 1, i: 1, g: 5} to form a word, what is the expected number of matches of the pattern 'dd+'? 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 5 letters from the multiset {l: 4, j: 1, w: 1, s: 1, i: 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": "When randomly selecting 5 letters from the multiset {z: 2, g: 2, x: 2, v: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'o*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 4, y: 2, x: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'dx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 5, a: 3, v: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 1, d: 4, k: 3, r: 2}. What is the expected number of occurrences of the pattern 'r+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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 3, h: 2, n: 2, a: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'na*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 3, p: 4, g: 3}. What is the expected number of occurrences of the pattern 'h.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 3, c: 3, d: 2, e: 2}. 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 4, s: 4, h: 2}, what is the expected number of times the pattern 'hp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 1, f: 4, w: 3, r: 2}. 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 4, a: 3, v: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'fv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 2, k: 1, q: 1, a: 5, l: 1} to form a word, what is the expected number of matches of the pattern 'q*l'? 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 5 letters from the multiset {t: 4, g: 4, b: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 2, p: 1, i: 2, m: 2, u: 3}, what is the expected number of times the pattern 'pi*' 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 5 letters from the multiset {l: 3, f: 6, q: 1} to form a word, what is the expected number of matches of the pattern 'l.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 5, p: 5}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 1, f: 4, t: 5} to form a word, what is the expected number of matches of the pattern 'ht+'? 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 5 by randomly selecting letters from the multiset {f: 3, o: 4, s: 3}, what is the expected number of times the pattern 'f*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 2, z: 3, d: 2, p: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 4, h: 6}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 5, g: 5}. 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 7, u: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, k: 3, r: 4}. What is the expected number of occurrences of the pattern 'kj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 5, w: 3, i: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, f: 2, k: 2, q: 2, j: 2}, what is the expected number of times the pattern 'j+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 6, w: 4}. What is the expected number of occurrences of the pattern 'w.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 4, e: 1, s: 2, 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": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, r: 1, u: 3, d: 2, n: 1}, what is the expected number of times the pattern 'r.*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 5 by randomly selecting letters from the multiset {p: 5, l: 2, x: 3}, 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 6, z: 4}, what is the expected number of times the pattern 'qz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 2, p: 1, g: 3, l: 1, h: 3}, what is the expected number of times the pattern 'h+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 1, u: 1, g: 5, f: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'uo*'? 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 5 letters from the multiset {l: 4, k: 6} to form a word, what is the expected number of matches of the pattern 'l*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 2, q: 3, j: 4, h: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 2, v: 2, f: 2, r: 1, a: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 6, q: 4} 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, z: 4, u: 4}, what is the expected number of times the pattern 'p+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 3, u: 7} 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 2, n: 8} 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": "6.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 3, q: 7}, what is the expected number of times the pattern 'qe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.62", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 7, o: 3}. What is the expected number of occurrences of the pattern 'og*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 3, f: 2, i: 5}, what is the expected number of times the pattern 'f*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 2, x: 3, m: 5} to form a word, what is the expected number of matches of the pattern 'x*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 3, u: 7}. What is the expected number of occurrences of the pattern 'ou*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 4, r: 6}. What is the expected number of occurrences of the pattern 'rh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 3, x: 3, u: 4} 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": "2.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 1, b: 3, y: 1, t: 5} to form a word, what is the expected number of matches of the pattern 't.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 5, a: 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 2, e: 2, r: 3, s: 2, j: 1}, 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 2, v: 4, z: 4}, what is the expected number of times the pattern 'kz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 3, o: 1, l: 6} 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": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 4, x: 6}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, k: 3, n: 3, h: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, u: 2, r: 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": "0.49", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 1, w: 4, n: 2, h: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 3, b: 7} to form a word, what is the expected number of matches of the pattern 'll*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 1, u: 6, g: 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 2, l: 1, q: 3, z: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'zl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, u: 3, m: 2, n: 1, o: 2}, what is the expected number of times the pattern 'on+' 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 5 letters from the multiset {o: 3, s: 1, g: 2, a: 3, n: 1} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 3, i: 1, v: 2, n: 1, b: 3}, 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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 1, f: 3, p: 2, o: 2, r: 2}. What is the expected number of occurrences of the pattern 'r+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 6, r: 2, t: 2}. What is the expected number of occurrences of the pattern 'rt*' 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 5 by randomly selecting letters from the multiset {r: 4, w: 2, e: 4}, 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, a: 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, j: 6}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 2, l: 7, k: 1}. What is the expected number of occurrences of the pattern 'k*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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 3, c: 2, w: 2, x: 1, f: 2}. 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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 2, g: 4, t: 1, o: 2, b: 1}. 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, f: 6, d: 2}. What is the expected number of occurrences of the pattern 'y*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 2, u: 4, z: 3, x: 1}. What is the expected number of occurrences of the pattern 'uo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 1, r: 4, u: 3, w: 2}. What is the expected number of occurrences of the pattern 'g.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 4, l: 2, b: 3, y: 1}, what is the expected number of times the pattern 'g+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 6, b: 4} to form a word, what is the expected number of matches of the pattern 'gb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 4, t: 2, l: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 5, f: 5}. What is the expected number of occurrences of the pattern 'fa+' 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 5 by randomly selecting letters from the multiset {w: 2, l: 3, z: 5}, what is the expected number of times the pattern 'wz*' 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 5 letters from the multiset {o: 3, d: 4, x: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'x*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 1, i: 3, s: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'i+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, o: 3, n: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 3, r: 4, t: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 1, r: 2, f: 1, a: 2, p: 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 5 letters from the multiset {m: 4, q: 3, t: 3}. What is the expected number of occurrences of the pattern 't.*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 5 letters from the multiset {w: 3, l: 2, m: 1, s: 4}. What is the expected number of occurrences of the pattern 'mw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 6, r: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, w: 2, z: 3, d: 3}. What is the expected number of occurrences of the pattern 'z+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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 2, a: 1, v: 1, h: 3, l: 3}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 3, o: 3, h: 3, d: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 1, k: 1, z: 3, q: 3, h: 2}, what is the expected number of times the pattern 'z+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 2, r: 3, e: 4, v: 1}. What is the expected number of occurrences of the pattern 'te*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 4, v: 3, k: 1, m: 2}. What is the expected number of occurrences of the pattern 'v*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": "2.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 7, y: 3}, what is the expected number of times the pattern 'a+y' 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 5 letters from the multiset {a: 1, e: 1, q: 2, i: 3, j: 3}. What is the expected number of occurrences of the pattern 'j+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": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 2, f: 2, x: 5, y: 1}, what is the expected number of times the pattern 'f+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, d: 2, n: 6}. What is the expected number of occurrences of the pattern 'y*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, e: 4, g: 2}. What is the expected number of occurrences of the pattern 'e+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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 6, u: 2, y: 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 3, q: 2, h: 1, r: 2, k: 2}. What is the expected number of occurrences of the pattern 'kh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 5, a: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 1, x: 3, t: 6} to form a word, what is the expected number of matches of the pattern 'tw+'? 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 5 letters from the multiset {n: 2, q: 2, f: 1, d: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 6, f: 4}, what is the expected number of times the pattern 'fl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 1, a: 2, s: 3, o: 4}. 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": "2.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, q: 3, d: 3}. 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": "1.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 1, n: 5, b: 1, q: 1, l: 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 5 letters from the multiset {a: 1, b: 1, w: 4, y: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'wo+'? 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 5 letters from the multiset {x: 1, i: 1, o: 4, s: 1, t: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 2, v: 2, e: 2, w: 3, i: 1}. What is the expected number of occurrences of the pattern 'wq*' 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 5 letters from the multiset {v: 2, z: 1, y: 4, t: 3} 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, q: 3, n: 2, y: 2, u: 2}. What is the expected number of occurrences of the pattern 'u*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 6, k: 4} to form a word, what is the expected number of matches of the pattern 'kx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 2, g: 2, v: 4, r: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'uv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 1, a: 5, b: 4} to form a word, what is the expected number of matches of the pattern 'c*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.72", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 3, v: 7}. What is the expected number of occurrences of the pattern 'vp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.62", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 7, q: 3}, what is the expected number of times the pattern 'h*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 1, b: 4, w: 3, n: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 4, x: 3, j: 3}, what is the expected number of times the pattern 'mx+' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 2, n: 2, z: 3, g: 3}, what is the expected number of times the pattern 'nl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 3, v: 2, m: 3, l: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 3, z: 2, x: 2, r: 1, p: 2}, 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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 2, m: 1, q: 3, n: 2, p: 2}. 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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 2, l: 3, o: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'lx*'? 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 5 letters from the multiset {w: 2, a: 2, e: 1, p: 4, k: 1} to form a word, what is the expected number of matches of the pattern 'w*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 4, o: 3, d: 3}, what is the expected number of times the pattern 'e+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 3, t: 2, g: 4, e: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 2, w: 2, g: 2, f: 1, e: 3}, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 2, d: 4, n: 4} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 5, s: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'fo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.99", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 3, m: 2, u: 1, t: 2, 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 2, k: 3, q: 2, c: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 3, m: 3, s: 4}, what is the expected number of times the pattern 'gm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 2, e: 3, s: 1, t: 3, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*e'? 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 5 letters from the multiset {w: 3, v: 7}. What is the expected number of occurrences of the pattern 'vw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.62", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 7, g: 3} 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, d: 3, z: 4}. What is the expected number of occurrences of the pattern 'lz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, z: 3, i: 3, v: 1}, what is the expected number of times the pattern 'iv+' 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 5 by randomly selecting letters from the multiset {a: 5, j: 5}, what is the expected number of times the pattern 'aj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 4, r: 4, g: 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": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 2, k: 3, x: 1, l: 4}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, c: 4}, what is the expected number of times the pattern 'x+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, w: 2, g: 3}, what is the expected number of times the pattern 'w.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 2, i: 3, b: 1, h: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 1, i: 2, o: 2, q: 3, n: 2} to form a word, what is the expected number of matches of the pattern 'iq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 3, c: 2, b: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'ww*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 6, r: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 5, a: 5} to form a word, what is the expected number of matches of the pattern 'ra+'? 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 5 letters from the multiset {y: 2, r: 2, n: 3, j: 3} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 3, q: 3, f: 2, i: 2}. What is the expected number of occurrences of the pattern 'i*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 1, e: 2, l: 1, z: 6}. What is the expected number of occurrences of the pattern 'p.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 1, x: 4, b: 2, u: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 3, s: 3, i: 2, f: 2}. What is the expected number of occurrences of the pattern 'i*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 4, h: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 7, p: 3}. What is the expected number of occurrences of the pattern 'qp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 3, u: 2, b: 2, i: 1, k: 2}. What is the expected number of occurrences of the pattern 'f+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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 4, d: 2, u: 4}, what is the expected number of times the pattern 'j+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 3, j: 4, f: 3}. 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": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 3, l: 2, v: 1, c: 2, q: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 2, g: 3, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 5, q: 5}, what is the expected number of times the pattern 'uq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, p: 4, a: 4}, what is the expected number of times the pattern 'ai*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 3, w: 4, q: 3}, what is the expected number of times the pattern 'w+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 6, y: 4} to form a word, what is the expected number of matches of the pattern 'y+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 3, c: 2, x: 4, f: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 2, w: 2, j: 1, p: 4, o: 1} to form a word, what is the expected number of matches of the pattern 'w+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, l: 3, s: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 7, p: 3}. What is the expected number of occurrences of the pattern 'cp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, r: 4, s: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 5, b: 5} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 3, q: 2, o: 3, x: 1, e: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 3, p: 7} to form a word, what is the expected number of matches of the pattern 'p.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, o: 1, a: 5}. 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": "3.69", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 3, p: 2, h: 5} to form a word, what is the expected number of matches of the pattern 'p.*r'? 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 5 by randomly selecting letters from the multiset {q: 8, y: 2}, what is the expected number of times the pattern 'q+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, h: 5, z: 2}. What is the expected number of occurrences of the pattern 'z*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 2, z: 4, n: 2, y: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 4, c: 3, r: 3}, what is the expected number of times the pattern 'cr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 2, q: 3, u: 5}. What is the expected number of occurrences of the pattern 'c*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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 3, u: 2, t: 3, n: 2} to form a word, what is the expected number of matches of the pattern 't+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 1, l: 1, v: 2, r: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'v+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 4, p: 1, x: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'k.*x'? 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 5 by randomly selecting letters from the multiset {c: 5, a: 5}, what is the expected number of times the pattern 'c+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 5 by randomly selecting letters from the multiset {l: 1, z: 1, x: 2, w: 4, g: 2}, what is the expected number of times the pattern 'g.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 3, f: 7}. 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": "4.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, h: 1, t: 2, p: 1, o: 4}, what is the expected number of times the pattern 'pt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 1, b: 3, n: 2, x: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'nz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 6, p: 4}, 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": "2.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 4, x: 6}. What is the expected number of occurrences of the pattern 'x.*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": "2.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 4, x: 2, o: 1, b: 2, a: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 1, x: 1, q: 6, o: 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": "Form a word by randomly choosing 5 letters from the multiset {h: 2, q: 1, t: 1, k: 3, g: 3}. What is the expected number of occurrences of the pattern 't*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 5, d: 3, i: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 6, k: 4} 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 4, s: 3, k: 1, j: 1, l: 1}. 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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 3, c: 5, k: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 1, h: 3, c: 2, t: 4}, what is the expected number of times the pattern 'cs+' 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": "Form a word by randomly choosing 5 letters from the multiset {w: 3, v: 7}. What is the expected number of occurrences of the pattern 'vw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.62", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 3, l: 1, v: 3, r: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 1, f: 2, b: 2, j: 2, g: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 2, w: 3, y: 4, m: 1} to form a word, what is the expected number of matches of the pattern 'y+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 5, w: 5} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 2, r: 1, u: 2, g: 5} to form a word, what is the expected number of matches of the pattern 'r+h'? 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 5 letters from the multiset {z: 2, x: 8}. 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": "6.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 1, t: 2, u: 2, z: 2, w: 3}. 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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 1, y: 3, s: 1, o: 2, q: 3}. What is the expected number of occurrences of the pattern 'sb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 1, d: 6, r: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 3, b: 1, t: 2, d: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 7, h: 3}. What is the expected number of occurrences of the pattern 'h.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 3, h: 2, o: 4, m: 1} to form a word, what is the expected number of matches of the pattern 'h.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 2, f: 2, o: 2, i: 4}, what is the expected number of times the pattern 'o+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, d: 3, p: 1, c: 3}. What is the expected number of occurrences of the pattern 'p+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 5 letters from the multiset {l: 1, j: 2, n: 3, u: 1, i: 3}. What is the expected number of occurrences of the pattern 'in+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, o: 4, g: 4}, what is the expected number of times the pattern 'o*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 3, w: 1, a: 3, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 2, e: 3, j: 3, q: 2} to form a word, what is the expected number of matches of the pattern 'e*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 1, i: 2, d: 3, r: 2, g: 2}, what is the expected number of times the pattern 'y+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, d: 2, a: 3, j: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, m: 3, j: 2, o: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 3, v: 1, u: 2, n: 4} 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": "0.24", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 4, w: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'pv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 1, s: 1, w: 2, b: 4, n: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 6, k: 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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 2, k: 1, m: 3, y: 2, i: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 4, u: 5, w: 1} to form a word, what is the expected number of matches of the pattern 'w+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 4, w: 1, a: 2, n: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 1, q: 3, r: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'r*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 1, m: 5, n: 3, o: 1}. What is the expected number of occurrences of the pattern 'no*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 3, s: 3, f: 1, v: 2, w: 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": "Form a word by randomly choosing 5 letters from the multiset {y: 1, p: 1, o: 2, r: 3, a: 3}. What is the expected number of occurrences of the pattern 'ar*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 1, o: 2, c: 3, b: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'h+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 6, e: 4}, 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 5, w: 4, z: 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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 3, u: 4, s: 1, b: 1, i: 1}, 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 5 by randomly selecting letters from the multiset {h: 1, x: 5, k: 1, s: 3}, what is the expected number of times the pattern 's+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 3, z: 3, p: 2, u: 1, b: 1}. What is the expected number of occurrences of the pattern 'zu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 2, w: 3, b: 2, l: 2, c: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 2, n: 3, b: 2, t: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'st*'? 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 5 letters from the multiset {c: 2, f: 4, m: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 3, x: 3, z: 4} to form a word, what is the expected number of matches of the pattern 'zx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, u: 2, f: 2, o: 1, x: 3}, what is the expected number of times the pattern 'oh*' 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 5 letters from the multiset {c: 4, d: 6}. What is the expected number of occurrences of the pattern 'cd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 5, k: 5}. 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 3, j: 4, n: 3}, what is the expected number of times the pattern 'p*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 3, f: 1, d: 2, k: 3, g: 1}. What is the expected number of occurrences of the pattern 'tg+' in 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 5 by randomly selecting letters from the multiset {t: 4, s: 2, a: 2, i: 2}, what is the expected number of times the pattern 's+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, x: 3, n: 5}, what is the expected number of times the pattern 'x+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 5, f: 1, r: 4}, what is the expected number of times the pattern 'u*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 6, l: 4}, what is the expected number of times the pattern 'l.*h' appears? 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": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 4, t: 3, o: 3}, what is the expected number of times the pattern 'o.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 1, v: 5, o: 2, x: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 3, d: 2, v: 1, h: 1, p: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 2, u: 3, j: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'u.*j'? 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 5 by randomly selecting letters from the multiset {m: 1, v: 2, i: 2, p: 3, r: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 1, m: 1, e: 3, t: 2, q: 3}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 4, d: 1, y: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'p*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 7, w: 3}, 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": "3.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 5, w: 5}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 3, f: 4, u: 3} to form a word, what is the expected number of matches of the pattern 'fv+'? 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 5 letters from the multiset {g: 1, i: 5, z: 3, f: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 2, u: 2, w: 5, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*u'? 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 5 letters from the multiset {b: 2, k: 2, d: 6} to form a word, what is the expected number of matches of the pattern 'dd+'? 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 5 letters from the multiset {a: 4, m: 3, o: 2, n: 1}. What is the expected number of occurrences of the pattern 'na*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 2, w: 2, e: 3, f: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, d: 5, u: 2, j: 1}. What is the expected number of occurrences of the pattern 'dj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.72", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, l: 3, s: 4}. What is the expected number of occurrences of the pattern 'js+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 2, w: 2, t: 3, k: 1, c: 2}. What is the expected number of occurrences of the pattern 'wk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 1, c: 6, p: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 4, t: 6}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 7, b: 3}, what is the expected number of times the pattern 'xb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 2, k: 2, w: 4, r: 2}. What is the expected number of occurrences of the pattern 'w.*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": "0.89", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 3, a: 3, z: 1, f: 2, m: 1}, what is the expected number of times the pattern 'f+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, a: 4, u: 2}. What is the expected number of occurrences of the pattern 'u.*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": "0.89", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 6, x: 4} to form a word, what is the expected number of matches of the pattern 'x+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 4, w: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 3, r: 1, g: 1, h: 5} to form a word, what is the expected number of matches of the pattern 'h.*b'? 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 5 by randomly selecting letters from the multiset {d: 3, x: 5, s: 2}, what is the expected number of times the pattern 'xd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 1, s: 3, a: 2, j: 2, y: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 5, c: 5}, what is the expected number of times the pattern 'cf+' 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 5 letters from the multiset {n: 1, t: 2, f: 7} to form a word, what is the expected number of matches of the pattern 'f.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 2, c: 3, n: 1, f: 3, r: 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 2, q: 4, p: 2, y: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 4, h: 1, b: 3, d: 2}. What is the expected number of occurrences of the pattern 'i+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": "0.24", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 5, g: 5}. 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": "4.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 4, h: 6} to form a word, what is the expected number of matches of the pattern 's+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 5, c: 3, u: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 4, e: 6} 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 3, z: 4, t: 3} to form a word, what is the expected number of matches of the pattern 'z+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 4, r: 1, l: 2, j: 2, o: 1}, what is the expected number of times the pattern 'lj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 4, h: 2, 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": "2.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 1, a: 3, f: 3, o: 2, y: 1}, what is the expected number of times the pattern 'f.*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 5 letters from the multiset {y: 2, n: 1, g: 3, e: 4} to form a word, what is the expected number of matches of the pattern 'g*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 3, y: 3, c: 4}. 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 5, r: 5}. What is the expected number of occurrences of the pattern 'zr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 3, d: 3, u: 1, p: 2, s: 1} 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": "0.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 3, m: 4, e: 3} to form a word, what is the expected number of matches of the pattern 'e*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 3, p: 4, t: 3} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 2, h: 2, l: 6} to form a word, what is the expected number of matches of the pattern 'j*h'? 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 5 letters from the multiset {g: 4, r: 3, o: 3}. 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 4, l: 6} 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": "4.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 4, s: 2, c: 2, q: 2}, what is the expected number of times the pattern 'q*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 1, y: 2, j: 3, w: 2, m: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 2, o: 3, a: 2, y: 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": "0.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 5, a: 5} to form a word, what is the expected number of matches of the pattern 'a*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 4, f: 1, h: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'hg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 1, b: 5, r: 4}. 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": "0.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, d: 2, t: 3, o: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, i: 1, s: 2, w: 2, o: 2}. What is the expected number of occurrences of the pattern 'k.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 4, w: 6}. What is the expected number of occurrences of the pattern 'k+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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 2, o: 1, d: 3, l: 2, v: 2} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 7, o: 3}. What is the expected number of occurrences of the pattern 'ou+' 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 5 letters from the multiset {y: 3, d: 2, v: 5} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 8, r: 2}. What is the expected number of occurrences of the pattern 'g+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 3, m: 2, p: 3, l: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'm*w'? 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 5 letters from the multiset {o: 1, c: 3, p: 3, b: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'fc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 6, a: 4}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, g: 3, n: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 4, x: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'xw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, d: 2, j: 1, q: 4, i: 1}, what is the expected number of times the pattern 'i*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 6, b: 4}. What is the expected number of occurrences of the pattern 'c*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, e: 2, d: 2, t: 3}. What is the expected number of occurrences of the pattern 'k*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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, y: 5, r: 2, b: 1}. What is the expected number of occurrences of the pattern 'r*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 5 letters from the multiset {e: 2, f: 2, c: 4, i: 2}. What is the expected number of occurrences of the pattern 'ce*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 6, f: 1, y: 3}, what is the expected number of times the pattern 'yf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 4, g: 2, h: 2, l: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 1, h: 3, w: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'w+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 7, c: 3}. What is the expected number of occurrences of the pattern 'v*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 3, r: 1, h: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'l*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 1, r: 3, u: 3, m: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'rv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 4, y: 3, p: 3}. What is the expected number of occurrences of the pattern 'yx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 2, i: 3, z: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 5, w: 5} to form a word, what is the expected number of matches of the pattern 'w*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, f: 3, y: 2, a: 1, i: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 3, x: 2, q: 5}, what is the expected number of times the pattern 'r.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 4, z: 1, n: 2, f: 2, k: 1}. What is the expected number of occurrences of the pattern 'z*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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 4, f: 4, h: 2} 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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, d: 3, z: 1, l: 4}, what is the expected number of times the pattern 'zb*' 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 5 letters from the multiset {n: 3, s: 1, r: 4, a: 2}. What is the expected number of occurrences of the pattern 'a*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 3, d: 3, i: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 1, z: 3, x: 6} to form a word, what is the expected number of matches of the pattern 'z*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.96", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 5, t: 5}. 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 3, b: 2, w: 2, e: 2, f: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, q: 3, r: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 2, w: 2, t: 2, e: 4}, 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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 8, e: 2} to form a word, what is the expected number of matches of the pattern 'o+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 5, i: 5} to form a word, what is the expected number of matches of the pattern 'i+b'? 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 5 letters from the multiset {j: 2, o: 4, h: 1, m: 2, i: 1}. What is the expected number of occurrences of the pattern 'j.*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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 3, c: 1, z: 3, k: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 3, t: 5, x: 2} to form a word, what is the expected number of matches of the pattern 'tf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 7, j: 3} to form a word, what is the expected number of matches of the pattern 'j*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.63", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 5, j: 5}, 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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, n: 5}, 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 6, q: 4}, what is the expected number of times the pattern 'i+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 4, k: 6}. 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": "2.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 3, x: 2, e: 2, b: 2, k: 1}, what is the expected number of times the pattern 'x*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 2, d: 2, j: 3, n: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 2, q: 5, c: 3}. What is the expected number of occurrences of the pattern 'q*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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 1, a: 5, d: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'dt+'? 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 5 by randomly selecting letters from the multiset {r: 2, s: 2, i: 1, j: 1, m: 4}, 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": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, w: 5}, 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": "2.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 2, w: 6, k: 2}. What is the expected number of occurrences of the pattern 'w*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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 2, c: 4, e: 4}, 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": "2.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 5, a: 5}. What is the expected number of occurrences of the pattern 'ap+' 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 5 by randomly selecting letters from the multiset {t: 2, e: 3, g: 3, o: 2}, what is the expected number of times the pattern 'g+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, l: 2, x: 2, i: 3}, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 1, d: 3, j: 3, b: 1, r: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 2, a: 2, n: 6}, what is the expected number of times the pattern 'z+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 2, t: 4, h: 3, i: 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 3, x: 4, c: 3} to form a word, what is the expected number of matches of the pattern 'cx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 7, b: 3}. 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": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 3, c: 2, i: 5}, what is the expected number of times the pattern 'i.*c' 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 5 letters from the multiset {b: 3, g: 3, n: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'g*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 4, n: 1, k: 1, i: 4} 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 5, x: 2, t: 3}. What is the expected number of occurrences of the pattern 't+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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 3, z: 2, d: 3, m: 2}. What is the expected number of occurrences of the pattern 'm+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": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 4, z: 2, u: 4}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 4, v: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'qv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 6, k: 3, y: 1}. 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 5 letters from the multiset {q: 2, l: 3, m: 5}. What is the expected number of occurrences of the pattern 'ql+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 7, t: 3}, what is the expected number of times the pattern 'st+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 2, e: 2, y: 1, b: 3, t: 2}. What is the expected number of occurrences of the pattern 'c.*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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 1, s: 2, y: 4, c: 3}. 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 1, z: 2, l: 2, y: 1, t: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 2, o: 2, i: 2, e: 4}, what is the expected number of times the pattern 'oa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 4, h: 3, s: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 4, b: 1, f: 1, n: 1, i: 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 6, d: 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, s: 4}, 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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 2, s: 1, q: 4, f: 2, h: 1}. What is the expected number of occurrences of the pattern 'oq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 4, j: 1, p: 2, m: 2, k: 1}. 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 1, k: 4, l: 1, n: 3, r: 1}. What is the expected number of occurrences of the pattern 'k+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 3, w: 2, f: 2, r: 2, o: 1}. What is the expected number of occurrences of the pattern 'w+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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 5, i: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'wp*'? 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 5 by randomly selecting letters from the multiset {m: 3, d: 1, i: 2, n: 2, h: 2}, 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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 2, f: 4, c: 4}, what is the expected number of times the pattern 'cf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 3, u: 3, e: 2, k: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 4, i: 1, l: 2, p: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 1, a: 3, n: 2, i: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'an*'? 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 5 letters from the multiset {j: 5, q: 5} to form a word, what is the expected number of matches of the pattern 'qj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 6, f: 4}, what is the expected number of times the pattern 'fo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 3, z: 4, w: 3} to form a word, what is the expected number of matches of the pattern 'w+z'? 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 5 letters from the multiset {j: 7, q: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 3, a: 3, i: 2, j: 2}. What is the expected number of occurrences of the pattern 'ua*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, b: 3, n: 2, k: 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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 7, q: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 2, x: 4, f: 2, a: 2}. What is the expected number of occurrences of the pattern 'pf*' 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 5 by randomly selecting letters from the multiset {s: 3, f: 5, 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": "0.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 1, f: 6, d: 3}, what is the expected number of times the pattern 'ed*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 3, o: 2, x: 2, z: 3}. What is the expected number of occurrences of the pattern 'a*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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 5, a: 5}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 1, i: 2, z: 2, p: 3, v: 2}, 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 4, i: 6}, 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 7, y: 3}. What is the expected number of occurrences of the pattern 'd+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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, t: 3, o: 1, p: 2}, what is the expected number of times the pattern 'po*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 2, t: 3, n: 5}. What is the expected number of occurrences of the pattern 'n*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": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 5, j: 5}, what is the expected number of times the pattern 'jb+' 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 5 by randomly selecting letters from the multiset {j: 3, q: 7}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 3, t: 1, u: 2, k: 2, q: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, a: 8}. What is the expected number of occurrences of the pattern 's+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": "0.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, e: 2, p: 3, l: 1}, what is the expected number of times the pattern 'el+' 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 5 letters from the multiset {z: 4, o: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'zo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 2, w: 2, e: 5, k: 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 4, d: 2, e: 1, z: 3} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 3, r: 1, l: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'l*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 2, t: 3, x: 3, j: 2}, 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": "0.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 4, c: 2, l: 2, q: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 2, e: 8}. What is the expected number of occurrences of the pattern 'eo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 4, c: 6}, 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 1, u: 4, t: 2, x: 2, r: 1}. What is the expected number of occurrences of the pattern 'up+' in 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 5 by randomly selecting letters from the multiset {f: 2, p: 8}, 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": "6.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, z: 2, u: 3, q: 3}. What is the expected number of occurrences of the pattern 'u+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 5, v: 1, n: 1, p: 2, f: 1}, what is the expected number of times the pattern 'n.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 6, t: 4} to form a word, what is the expected number of matches of the pattern 'tg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 2, o: 1, w: 4, m: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'ow+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 6, v: 4} to form a word, what is the expected number of matches of the pattern 'v+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 4, y: 6}, what is the expected number of times the pattern 'f+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 2, v: 3, o: 2, i: 1, c: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 4, d: 6}, what is the expected number of times the pattern 'dc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 2, z: 4, a: 4}. 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 4, t: 6}, 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 5, e: 5}, what is the expected number of times the pattern 'n+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 5, d: 5} to form a word, what is the expected number of matches of the pattern 'd.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 2, f: 3, n: 5} to form a word, what is the expected number of matches of the pattern 't+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 2, h: 3, u: 1, p: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'pz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, c: 9}. 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, j: 5, k: 3}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 1, m: 1, e: 1, s: 3, a: 4}. What is the expected number of occurrences of the pattern 'e+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 3, d: 6, h: 1}. What is the expected number of occurrences of the pattern 'h.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 4, l: 2, c: 2, s: 2}. What is the expected number of occurrences of the pattern 'l.*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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 3, g: 7}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 1, w: 4, m: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 3, b: 2, y: 2, v: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'n.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 7, s: 3}, what is the expected number of times the pattern 'sp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 1, b: 3, n: 4, m: 2}. 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": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 4, d: 6}. What is the expected number of occurrences of the pattern 'm.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, k: 3, d: 5}. What is the expected number of occurrences of the pattern 'd*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 6, d: 4} to form a word, what is the expected number of matches of the pattern 'd+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 2, a: 7, s: 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": "Form a word by randomly choosing 5 letters from the multiset {n: 5, s: 5}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 2, m: 1, d: 3, x: 2, l: 2}. What is the expected number of occurrences of the pattern 'mx*' in 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": "When randomly selecting 5 letters from the multiset {t: 4, d: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'd+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 3, h: 5, q: 2}, what is the expected number of times the pattern 'h.*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 5 letters from the multiset {p: 2, q: 4, e: 2, n: 2}. 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 2, w: 2, h: 2, d: 1, i: 3} to form a word, what is the expected number of matches of the pattern 'iw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 1, b: 3, i: 5, z: 1} 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, i: 3, w: 3, n: 2}, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 2, s: 3, i: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'i+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, t: 4, c: 1, o: 2}, what is the expected number of times the pattern 'om+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 4, b: 6}, 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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 7, t: 3} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 3, z: 4, e: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 1, t: 2, h: 2, w: 3, d: 2}, what is the expected number of times the pattern 'w.*h' 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 5 letters from the multiset {m: 2, k: 3, h: 5}. What is the expected number of occurrences of the pattern 'm+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": "0.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 4, o: 6}, 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 2, r: 2, z: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'ra*'? 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 5 letters from the multiset {y: 3, p: 1, c: 1, b: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'c.*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": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 1, d: 4, a: 3, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 3, x: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'xu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, b: 2, j: 1, p: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, f: 2, d: 4, s: 2}, what is the expected number of times the pattern 'f+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 5, k: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 5, j: 2, q: 3}. What is the expected number of occurrences of the pattern 'q*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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 5, u: 5} to form a word, what is the expected number of matches of the pattern 'o.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 2, v: 3, i: 2, s: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'si+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 4, y: 6} to form a word, what is the expected number of matches of the pattern 'y.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 1, f: 1, m: 4, o: 2, i: 2}. What is the expected number of occurrences of the pattern 'o+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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 4, w: 6}, what is the expected number of times the pattern 'w+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 4, u: 2, b: 4} 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 3, a: 3, x: 2, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 2, e: 2, c: 2, i: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'ec+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, o: 2, h: 3, z: 3}, what is the expected number of times the pattern 'o*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 1, r: 2, h: 3, s: 4}, what is the expected number of times the pattern 'ro+' 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 5 by randomly selecting letters from the multiset {c: 3, n: 1, t: 3, s: 2, q: 1}, 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 5, r: 1, n: 1, u: 2, o: 1}. What is the expected number of occurrences of the pattern 'o*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": "0.54", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 4, t: 2, q: 4}, 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": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 1, x: 3, w: 1, t: 1, v: 4}, what is the expected number of times the pattern 'h+t' 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": "Form a word by randomly choosing 5 letters from the multiset {i: 1, v: 3, s: 1, e: 2, t: 3}. What is the expected number of occurrences of the pattern 't.*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": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, o: 2, x: 1, s: 4, f: 1}, what is the expected number of times the pattern 'xp*' 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 5 letters from the multiset {e: 5, n: 3, c: 2} 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 6, f: 4} to form a word, what is the expected number of matches of the pattern 'pf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 3, b: 2, q: 2, k: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 4, k: 6} to form a word, what is the expected number of matches of the pattern 'mk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 5, t: 5}, what is the expected number of times the pattern 'tp+' 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 5 by randomly selecting letters from the multiset {h: 2, o: 1, x: 1, z: 2, f: 4}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, m: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 3, c: 5, y: 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": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 6, d: 4}. 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": "2.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 2, i: 2, x: 2, b: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'e*i'? 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 5 letters from the multiset {o: 4, y: 6}. 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, x: 3, w: 2, v: 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 4, t: 1, y: 5} to form a word, what is the expected number of matches of the pattern 't*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 6, o: 1, w: 2, k: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 2, v: 2, u: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'u.*l'? 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 5 letters from the multiset {n: 3, v: 1, p: 2, x: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'n+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 7, b: 3}, what is the expected number of times the pattern 's+b' 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 5 letters from the multiset {v: 2, s: 1, q: 4, z: 3} 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": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 4, j: 6}. What is the expected number of occurrences of the pattern 'jb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 4, j: 4, m: 2}, what is the expected number of times the pattern 't.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 3, u: 7}. What is the expected number of occurrences of the pattern 'z+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": "1.12", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 4, a: 6} 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": "2.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, v: 4, f: 2, r: 2}, what is the expected number of times the pattern 'c*r' 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 5 letters from the multiset {n: 1, x: 2, q: 3, p: 4} to form a word, what is the expected number of matches of the pattern 'p*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, d: 3, h: 2, c: 2}. 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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, a: 5}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 3, a: 2, y: 2, l: 2, n: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 5, k: 1, s: 2, q: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 5, g: 5} 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 1, g: 1, l: 1, w: 4, v: 3}, what is the expected number of times the pattern 'ly+' 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 5 letters from the multiset {m: 4, r: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'r.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 1, x: 3, i: 3, n: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'ki*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 2, s: 3, g: 2, z: 1, t: 2}. 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 2, s: 2, q: 2, h: 3, k: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 4, u: 2, e: 2, c: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 1, j: 3, k: 1, a: 2, r: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 2, m: 3, w: 3, t: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, c: 1, e: 2, w: 2, d: 2}. What is the expected number of occurrences of the pattern 'lc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, j: 5, n: 2}, what is the expected number of times the pattern 'wj+' 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 5 letters from the multiset {q: 1, s: 4, k: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'ks+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 2, e: 3, s: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'ey+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, x: 2, r: 1, i: 3, n: 2}, what is the expected number of times the pattern 'sn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 3, q: 2, k: 2, p: 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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 2, z: 2, d: 2, g: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'gz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, z: 6}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 2, c: 2, t: 4, i: 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": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, x: 5, o: 3}. What is the expected number of occurrences of the pattern 'x*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 5 letters from the multiset {d: 5, 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, u: 2, f: 5}. What is the expected number of occurrences of the pattern 'uf+' in 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 5 letters from the multiset {s: 4, d: 4, y: 2}. What is the expected number of occurrences of the pattern 's+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 2, q: 1, w: 1, h: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'h.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.89", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, h: 3}, what is the expected number of times the pattern 'h.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 4, c: 6}, 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": "4.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 2, t: 8} 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": "6.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 3, r: 2, x: 1, d: 4}. What is the expected number of occurrences of the pattern 'xg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 2, u: 2, j: 2, f: 2, g: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, y: 4, n: 2}, what is the expected number of times the pattern 'd*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, q: 3, x: 2, u: 1, b: 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": "0.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, k: 3, v: 5}, what is the expected number of times the pattern 'wv+' 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 5 letters from the multiset {y: 3, m: 1, s: 3, x: 3}. 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": "0.66", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 3, t: 2, l: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*b'? 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 5 letters from the multiset {k: 2, x: 3, g: 2, r: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'r*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 3, x: 7} to form a word, what is the expected number of matches of the pattern 'xb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.12", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 3, n: 1, l: 3, k: 3}, what is the expected number of times the pattern 'no+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 2, h: 2, b: 2, n: 3, o: 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 4, f: 2, e: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'ep*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 2, s: 3, q: 1, r: 3, x: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 3, z: 2, g: 3, c: 2}. What is the expected number of occurrences of the pattern 'gu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 4, l: 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": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 3, z: 2, m: 1, j: 4}, what is the expected number of times the pattern 'z+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 4, i: 2, l: 4}. What is the expected number of occurrences of the pattern 'im+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 4, y: 6} to form a word, what is the expected number of matches of the pattern 'zy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 7, g: 3} to form a word, what is the expected number of matches of the pattern 'gp+'? 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 5 letters from the multiset {q: 3, z: 4, u: 2, v: 1} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 3, a: 3, z: 4} to form a word, what is the expected number of matches of the pattern 'z.*u'? 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 5 by randomly selecting letters from the multiset {w: 3, b: 4, e: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 2, i: 1, r: 3, y: 3, w: 1}. 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, t: 1, y: 3, h: 3, a: 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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 1, i: 1, a: 4, h: 2, x: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 6, d: 4}. 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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 1, h: 3, x: 3, d: 1, o: 2}. 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 4, w: 1, q: 2, e: 2, n: 1}. 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 2, x: 5, n: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 3, o: 3, s: 1, u: 2, c: 1}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 4, i: 3, w: 3}, what is the expected number of times the pattern 'i*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 3, p: 6, f: 1} 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 3, u: 4, a: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 6, u: 4} 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 5, p: 5}. What is the expected number of occurrences of the pattern 'x.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 1, b: 2, j: 1, y: 3, k: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 1, d: 4, j: 4, w: 1}, what is the expected number of times the pattern 'd+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 7, w: 3} to form a word, what is the expected number of matches of the pattern 'tw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.63", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, n: 3, e: 1, j: 2, t: 1}, what is the expected number of times the pattern 'tn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 3, i: 5, b: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 2, r: 1, w: 1, o: 3, h: 3}, what is the expected number of times the pattern 'w.*o' 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 5 by randomly selecting letters from the multiset {c: 3, f: 5, a: 1, d: 1}, what is the expected number of times the pattern 'c.*a' 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 5 by randomly selecting letters from the multiset {l: 5, y: 5}, what is the expected number of times the pattern 'l+y' 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 5 letters from the multiset {p: 6, v: 1, l: 3}. What is the expected number of occurrences of the pattern 'lv+' in 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 5 letters from the multiset {e: 3, l: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 3, u: 3, g: 4} to form a word, what is the expected number of matches of the pattern 'gu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 3, t: 1, z: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'i+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 3, t: 3, g: 2, u: 2}. What is the expected number of occurrences of the pattern 'x*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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 4, g: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'gu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, g: 4, j: 2, b: 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": "0.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 5, r: 3, y: 1, x: 1}. What is the expected number of occurrences of the pattern 'x*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 2, o: 8} to form a word, what is the expected number of matches of the pattern 'om*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.78", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 4, u: 6}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 3, n: 7}, what is the expected number of times the pattern 'n.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 4, s: 4, t: 2}. What is the expected number of occurrences of the pattern 't*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 5, f: 5} to form a word, what is the expected number of matches of the pattern 't*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 3, u: 4, w: 3}, what is the expected number of times the pattern 't.*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 5 by randomly selecting letters from the multiset {h: 1, o: 4, i: 3, z: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 4, i: 4, x: 1, q: 1}. What is the expected number of occurrences of the pattern 'xq*' in 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 5 letters from the multiset {k: 3, v: 1, e: 6}. What is the expected number of occurrences of the pattern 'ke+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.35", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 4, a: 5, x: 1} to form a word, what is the expected number of matches of the pattern 'a+n'? 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 5 letters from the multiset {t: 1, a: 4, g: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'gt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 6, w: 4}, what is the expected number of times the pattern 's.*w' appears? 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": "When randomly selecting 5 letters from the multiset {f: 4, l: 6} to form a word, what is the expected number of matches of the pattern 'f*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 1, n: 4, f: 2, r: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, q: 4, l: 2, d: 1}. What is the expected number of occurrences of the pattern 'l+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 2, f: 1, i: 4, v: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 2, m: 4, t: 2, s: 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": "1.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 3, f: 3, j: 4}. What is the expected number of occurrences of the pattern 'jf+' in 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 5 letters from the multiset {r: 4, h: 3, z: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'h*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 4, r: 1, t: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'f+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 3, z: 3, e: 4} to form a word, what is the expected number of matches of the pattern 'e+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 3, e: 1, f: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 7, l: 3}. What is the expected number of occurrences of the pattern 'dl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 3, v: 2, k: 3, m: 2}, what is the expected number of times the pattern 'rm*' 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 5 letters from the multiset {f: 3, b: 7} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 4, v: 2, w: 4} 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": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 2, s: 1, f: 2, g: 2, r: 3} 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 7, x: 3} 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": "4.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 1, p: 2, d: 6, g: 1}. 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 4, i: 2, l: 1, s: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 5, x: 5}, what is the expected number of times the pattern 'xy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 6, e: 4}. What is the expected number of occurrences of the pattern 'e+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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 4, t: 4, f: 2}, what is the expected number of times the pattern 't+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 6, r: 2, v: 2}. 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 1, h: 5, i: 2, t: 2}. What is the expected number of occurrences of the pattern 't*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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 5, s: 5} 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": "2.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 3, x: 3, d: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 3, k: 3, c: 4} to form a word, what is the expected number of matches of the pattern 'cu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 2, t: 1, l: 2, e: 3, k: 2} to form a word, what is the expected number of matches of the pattern 't*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 3, y: 2, p: 3, l: 2} 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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 3, a: 4, n: 1, 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 4, p: 6} to form a word, what is the expected number of matches of the pattern 'vp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 6, q: 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": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 1, u: 3, q: 1, r: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'xq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 3, t: 3, b: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 4, q: 6}, 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 1, r: 2, g: 1, a: 4, x: 2}. What is the expected number of occurrences of the pattern 'a+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": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 4, q: 4, z: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, z: 5, i: 1}, what is the expected number of times the pattern 'zi+' 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": "Form a word by randomly choosing 5 letters from the multiset {q: 3, z: 3, j: 2, p: 2}. What is the expected number of occurrences of the pattern 'j*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": "1.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 2, p: 3, l: 1, i: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'pl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 7, y: 3} 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 4, h: 6}. What is the expected number of occurrences of the pattern 'h.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 7, i: 3}. What is the expected number of occurrences of the pattern 'i.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 3, g: 7} to form a word, what is the expected number of matches of the pattern 'p.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 5, f: 5}. What is the expected number of occurrences of the pattern 'f*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": "4.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 1, n: 2, q: 2, h: 4, t: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 2, b: 2, m: 2, q: 2, o: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 1, b: 2, g: 4, 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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 2, m: 2, f: 2, u: 3, n: 1}. What is the expected number of occurrences of the pattern 'u.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 4, m: 4, c: 1, l: 1}, what is the expected number of times the pattern 'cr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 4, r: 3, n: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'rm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 4, f: 6} to form a word, what is the expected number of matches of the pattern 'a+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 4, e: 3, i: 3}, what is the expected number of times the pattern 'i+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 2, t: 3, b: 1, o: 4} to form a word, what is the expected number of matches of the pattern 't.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 5, r: 2, u: 2, t: 1}, what is the expected number of times the pattern 'tu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, w: 3, c: 3, p: 2}, what is the expected number of times the pattern 'p+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 2, l: 4, p: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 2, c: 3, m: 5} to form a word, what is the expected number of matches of the pattern 'c*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 4, x: 3, z: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, r: 4, u: 2, h: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 3, e: 2, g: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'xg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 5, a: 5}. What is the expected number of occurrences of the pattern 'ra+' 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 5 letters from the multiset {v: 1, c: 3, y: 1, f: 3, l: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, e: 3, p: 3, u: 1}. 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 1, e: 1, g: 3, d: 3, l: 2}. What is the expected number of occurrences of the pattern 'e+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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, c: 2, a: 1, b: 3, f: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 2, e: 8}, what is the expected number of times the pattern 'l+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 6, u: 4} 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 4, a: 1, t: 3, e: 1, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 5, u: 5}. What is the expected number of occurrences of the pattern 'u*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": "4.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, e: 2, g: 3, u: 2}. What is the expected number of occurrences of the pattern 'g*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": "1.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, u: 1, f: 2, j: 4, x: 1}. What is the expected number of occurrences of the pattern 'u.*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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 3, j: 2, l: 1, i: 1, b: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, d: 3, o: 2, z: 1, y: 2}, what is the expected number of times the pattern 's+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 3, o: 2, c: 2, z: 3} 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": "1.98", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 2, o: 2, e: 3, f: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 2, v: 3, r: 3, j: 2} to form a word, what is the expected number of matches of the pattern 'j*v'? 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 5 letters from the multiset {b: 4, t: 1, q: 3, a: 2}. 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": "2.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 1, k: 1, r: 2, z: 1, s: 5}. What is the expected number of occurrences of the pattern 'wz*' in 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 5 letters from the multiset {d: 7, g: 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": "4.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 2, e: 5, y: 3}, what is the expected number of times the pattern 'y+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 2, a: 1, n: 2, v: 1, g: 4}. What is the expected number of occurrences of the pattern 'a+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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 3, n: 2, e: 1, c: 3, b: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, g: 4, k: 3, h: 1}, what is the expected number of times the pattern 'hg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 1, y: 2, s: 2, o: 4, d: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 5, q: 5} to form a word, what is the expected number of matches of the pattern 'xq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 3, c: 5, g: 2}. What is the expected number of occurrences of the pattern 'co*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 4, g: 3, d: 3}, what is the expected number of times the pattern 'gj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 2, y: 2, z: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, j: 3, c: 4}, 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": "0.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 5, p: 5}, what is the expected number of times the pattern 'pn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 7, v: 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": "4.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, d: 2, e: 6}, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 3, q: 4, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 1, t: 2, y: 4, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 4, y: 1, a: 3, d: 1, b: 1} 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 5 letters from the multiset {u: 4, k: 5, g: 1}. 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 2, e: 1, k: 3, h: 4}, what is the expected number of times the pattern 'm+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, t: 1, p: 1, s: 3}, what is the expected number of times the pattern 'tp*' 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": "Form a word by randomly choosing 5 letters from the multiset {f: 2, c: 3, z: 3, j: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, a: 3, v: 2, t: 2, q: 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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 7, t: 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": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 2, x: 4, n: 2, k: 1, z: 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 3, l: 4, w: 3} to form a word, what is the expected number of matches of the pattern 'lo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 5, d: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 5, n: 3, e: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 3, z: 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": "2.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 1, l: 4, q: 2, i: 3}, 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": "0.74", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 7, x: 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": "4.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 3, s: 4, d: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 2, t: 5, b: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'k*l'? 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 5 by randomly selecting letters from the multiset {o: 6, k: 4}, what is the expected number of times the pattern 'ok*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 2, w: 4, c: 4} to form a word, what is the expected number of matches of the pattern 'j*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 3, j: 5, m: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, j: 2, s: 2, e: 3, k: 1}. What is the expected number of occurrences of the pattern 'ej+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 5, a: 5}, what is the expected number of times the pattern 'ga*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 2, k: 3, p: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, n: 4, h: 1, d: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 3, x: 2, c: 4, 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": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, j: 4}, what is the expected number of times the pattern 'd*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 1, c: 6, w: 3}. What is the expected number of occurrences of the pattern 'wc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.35", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 6, s: 4}. What is the expected number of occurrences of the pattern 'n+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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 4, r: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'dr+'? 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 5 letters from the multiset {c: 1, j: 1, z: 5, y: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'a*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.72", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, c: 2, x: 1, o: 4, s: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 3, k: 2, m: 3, w: 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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {j: 5, d: 5}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 1, p: 4, o: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'up+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 3, n: 3, e: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'n*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 4, m: 1, v: 2, n: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 2, c: 1, x: 2, y: 1, v: 4}. What is the expected number of occurrences of the pattern 'v*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": "1.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 3, k: 4, r: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, l: 2, p: 1, i: 3, t: 2}. What is the expected number of occurrences of the pattern 'i*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, o: 3, m: 3, l: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, z: 3, u: 2, x: 1, o: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 1, n: 3, w: 4, s: 2}. What is the expected number of occurrences of the pattern 'l.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {a: 2, s: 4, t: 3, l: 1} to form a word, what is the expected number of matches of the pattern 's+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 6, d: 4} to form a word, what is the expected number of matches of the pattern 'd+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 1, a: 5, x: 4} to form a word, what is the expected number of matches of the pattern 'e.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 2, c: 2, e: 1, n: 2, g: 3}, what is the expected number of times the pattern 'l.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, o: 4, v: 2, e: 2}, what is the expected number of times the pattern 'ho+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 4, f: 6}. What is the expected number of occurrences of the pattern 'k*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, i: 9}. 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": "8.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, m: 1, o: 3, p: 1, j: 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": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 3, o: 4, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 2, r: 2, e: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'd+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 7, u: 3} 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": "4.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 2, r: 1, h: 3, u: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 2, r: 3, l: 3, i: 2}. What is the expected number of occurrences of the pattern 'ri*' 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 5 letters from the multiset {s: 5, i: 5} 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 4, b: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 3, q: 4, c: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, p: 3, o: 2, r: 2, t: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 5, b: 5} to form a word, what is the expected number of matches of the pattern 'h.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 1, u: 4, n: 2, a: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, p: 1, v: 6, w: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 3, k: 2, r: 1, c: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'rc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 1, a: 2, p: 3, t: 1, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, g: 7}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 2, o: 3, d: 2, b: 3} to form a word, what is the expected number of matches of the pattern 'o+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 2, q: 2, j: 2, a: 3, f: 1}. What is the expected number of occurrences of the pattern 'a.*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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 1, t: 3, l: 2, a: 3, x: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 5, r: 5}. What is the expected number of occurrences of the pattern 'dr+' 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 5 by randomly selecting letters from the multiset {w: 3, z: 3, d: 2, o: 2}, what is the expected number of times the pattern 'o*d' 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": "Form a word by randomly choosing 5 letters from the multiset {a: 2, y: 4, d: 2, k: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 6, p: 4} to form a word, what is the expected number of matches of the pattern 'w*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, m: 3, g: 1, h: 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 5, g: 3, d: 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": "2.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 1, a: 3, g: 2, w: 4}, what is the expected number of times the pattern 'wa+' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, z: 3, p: 5}, what is the expected number of times the pattern 'p*i' 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 5 letters from the multiset {k: 3, c: 3, o: 4} to form a word, what is the expected number of matches of the pattern 'k*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {w: 2, p: 1, m: 4, k: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'm+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 5, k: 5}, what is the expected number of times the pattern 'y.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.78", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 4, e: 6}. What is the expected number of occurrences of the pattern 'w+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": "1.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, s: 8}, 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": "4.78", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 3, s: 4, q: 3} 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": "0.48", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 1, v: 2, q: 2, r: 2, f: 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": "0.22", "dataset": "MATH"}