{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, w: 1, c: 1, l: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'uf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, y: 3, g: 2, a: 3}. What is the expected number of occurrences of the pattern 'e*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": "1.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, m: 1, y: 2, j: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'ym+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.06", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, f: 1, q: 1, i: 2, x: 2}, what is the expected number of times the pattern 'f*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, l: 3, a: 1, g: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'l+a'? 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 3 letters from the multiset {d: 2, f: 2, n: 4, o: 4}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, p: 1, r: 3, v: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 6, v: 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": "3.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 2, q: 7, k: 3} to form a word, what is the expected number of matches of the pattern 'kq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.72", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, d: 2, q: 2, f: 6} to form a word, what is the expected number of matches of the pattern 'f+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, v: 4, s: 1, e: 2, k: 1}, what is the expected number of times the pattern 'ue*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, v: 1, u: 5, c: 1}. What is the expected number of occurrences of the pattern 'c*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": "0.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 5, r: 3}, 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": "2.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, j: 2, r: 7} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, b: 1, f: 2, n: 2, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 4, u: 5} to form a word, what is the expected number of matches of the pattern 'du*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 7, y: 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, d: 2, m: 2, o: 6}. What is the expected number of occurrences of the pattern 'o+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": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 2, h: 3, m: 3, w: 4} 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": "0.55", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, k: 3, j: 1, r: 2, q: 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": "0.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 5, q: 1, u: 3, s: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 6, i: 2, s: 1, k: 1}. What is the expected number of occurrences of the pattern 'ki+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, r: 5}, what is the expected number of times the pattern 'ra+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, e: 1, z: 3, k: 4} to form a word, what is the expected number of matches of the pattern 'ze+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, b: 2, t: 2, q: 2, v: 3}. What is the expected number of occurrences of the pattern 'tt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, y: 4, g: 2, p: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'yp+'? 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 3 by randomly selecting letters from the multiset {t: 5, p: 3, v: 4}, what is the expected number of times the pattern 't*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 7, f: 3}, what is the expected number of times the pattern 'fz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, l: 5, v: 3} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 1, y: 3, d: 1, i: 3, v: 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": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, j: 3, a: 3, n: 1, o: 1}, what is the expected number of times the pattern 'a+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, p: 3, r: 1, x: 1, f: 1}, what is the expected number of times the pattern 'fh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, o: 1, h: 1, e: 2, i: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, q: 1, d: 3, x: 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": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, d: 1, g: 3, r: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'rg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, j: 3, a: 3, x: 2}, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, u: 4}. 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 1, c: 2, b: 2, a: 4, i: 2}. What is the expected number of occurrences of the pattern 'cy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 7, y: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, i: 4, r: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, g: 1, z: 3, j: 1, q: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 8, e: 4} to form a word, what is the expected number of matches of the pattern 'e.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 5, b: 2, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, q: 2, g: 2, m: 1}, what is the expected number of times the pattern 'a+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, f: 2, q: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 5, u: 7} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, r: 2, o: 3}, what is the expected number of times the pattern 'oz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 7, s: 4}. What is the expected number of occurrences of the pattern 's.*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": "1.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, x: 3, s: 2, z: 1, e: 2}. What is the expected number of occurrences of the pattern 'je*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 5, f: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'f.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, j: 2, i: 2, r: 1, k: 1}, what is the expected number of times the pattern 'i.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, t: 1, q: 2, z: 3, x: 3}, what is the expected number of times the pattern 'ct*' 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": "Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 3, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, r: 4, i: 3, o: 1}, what is the expected number of times the pattern 'oi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 6, n: 2}. What is the expected number of occurrences of the pattern 'y+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": "0.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, s: 2, c: 3, m: 2}, what is the expected number of times the pattern 'c*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 5, w: 4}. What is the expected number of occurrences of the pattern 'v*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": "2.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, o: 3, l: 1, e: 5}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 2, j: 3, z: 2, p: 5} to form a word, what is the expected number of matches of the pattern 'z.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 5, e: 3, w: 1}. What is the expected number of occurrences of the pattern 'q*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.26", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 5, k: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'xk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, s: 4} to form a word, what is the expected number of matches of the pattern 'a+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, q: 7}. What is the expected number of occurrences of the pattern 'q*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, u: 3, z: 4} to form a word, what is the expected number of matches of the pattern 'uz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, q: 4, s: 5} to form a word, what is the expected number of matches of the pattern 'sq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, k: 2, x: 4, i: 2}, what is the expected number of times the pattern 'ik*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 7, t: 4} 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": "0.76", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, q: 6, d: 4}. What is the expected number of occurrences of the pattern 'q*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": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 5, b: 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": "2.34", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 5, m: 4}, what is the expected number of times the pattern 'qm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.34", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 5, u: 5} to form a word, what is the expected number of matches of the pattern 'u+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 4, m: 4, o: 2}, what is the expected number of times the pattern 'z*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, j: 2, w: 1, e: 2, r: 2}. What is the expected number of occurrences of the pattern 'wj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, c: 5, t: 2, x: 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": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, b: 2, g: 4, o: 3}, what is the expected number of times the pattern 'ag+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 6, n: 6}, 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": "0.82", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, y: 2, e: 2, j: 1, b: 1} 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, n: 3, b: 1, u: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'tt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 6, q: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 3, x: 3, i: 1, y: 3, v: 2}. What is the expected number of occurrences of the pattern 'y*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": "0.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, r: 3, p: 1, e: 2, h: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 5, v: 1, g: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'g.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, h: 1, a: 4, q: 1, j: 2}. What is the expected number of occurrences of the pattern 'hn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, s: 4, d: 3}, what is the expected number of times the pattern 'd*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 6, w: 1, m: 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, b: 1, w: 2, s: 2}, what is the expected number of times the pattern 'ws*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, r: 1, i: 2, h: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'yi*'? 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 4 by randomly selecting letters from the multiset {u: 5, w: 2, i: 2, v: 1, p: 1}, what is the expected number of times the pattern 'vu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 3, x: 2, e: 2, a: 1, f: 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, k: 1, n: 6}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 4, y: 7}, what is the expected number of times the pattern 'w+y' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, c: 7, g: 4}, what is the expected number of times the pattern 's+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.06", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 4, m: 1, y: 3, t: 1}, what is the expected number of times the pattern 'y.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 6, t: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, r: 4, j: 5}, what is the expected number of times the pattern 'rq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, h: 5, n: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, t: 1, q: 2, g: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'gq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, w: 3, y: 3}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 3, x: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'x.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, y: 1, h: 3, v: 4}, 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 4, w: 3, u: 1}, what is the expected number of times the pattern 'o+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.03", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, r: 4, v: 2, c: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, g: 2, t: 3, z: 1, a: 4} to form a word, what is the expected number of matches of the pattern 'tz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 3, f: 2, o: 3, d: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 1, x: 1, o: 2, l: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, e: 2, z: 2, a: 3}. What is the expected number of occurrences of the pattern 'ze+' in 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 3 letters from the multiset {u: 4, v: 5}. What is the expected number of occurrences of the pattern 'uv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.05", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, o: 2, c: 3, y: 2, k: 3}, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, q: 2, u: 3, e: 1, i: 1}, what is the expected number of times the pattern 'iu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.38", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, j: 2, t: 2, d: 2, o: 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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, z: 2, o: 4}, what is the expected number of times the pattern 'zv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, y: 4}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 3, n: 4, z: 2}. What is the expected number of occurrences of the pattern 'g+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, t: 1, p: 1, y: 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": "1.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, w: 3, t: 3}, what is the expected number of times the pattern 't*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, n: 4, p: 3}. What is the expected number of occurrences of the pattern 'r*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 3, d: 1, l: 1, u: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'lu+'? 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 3 letters from the multiset {d: 6, r: 1, v: 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 5, m: 6}, what is the expected number of times the pattern 'x+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, t: 4, k: 2}, what is the expected number of times the pattern 'et*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 7, l: 5} 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": "1.59", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 3, e: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, i: 8} to form a word, what is the expected number of matches of the pattern 'i+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.61", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, o: 3, r: 1, c: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'r.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, h: 2, o: 5} to form a word, what is the expected number of matches of the pattern 'i.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 2, f: 1, j: 2, 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": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, u: 3, a: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'u.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, e: 1, c: 3, x: 3, v: 1}. What is the expected number of occurrences of the pattern 'fc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.04", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 5, u: 5}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, z: 7} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'js*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, h: 4, e: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'hw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 5, f: 6}, 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": "0.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, c: 2, b: 3, q: 3}. What is the expected number of occurrences of the pattern 'gg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, l: 1, z: 2, v: 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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 4, s: 6, z: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 1, t: 1, x: 2, q: 2, n: 2}, what is the expected number of times the pattern 'q.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, h: 2, j: 2, c: 3, y: 3}, what is the expected number of times the pattern 'jy+' 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 3 letters from the multiset {q: 4, d: 2, e: 2}. What is the expected number of occurrences of the pattern 'qe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.31", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, a: 2, k: 1, v: 4, j: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 6, r: 2} to form a word, what is the expected number of matches of the pattern 'rf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 9, z: 3}. What is the expected number of occurrences of the pattern 'z+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": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, z: 1, a: 2, h: 3, b: 2}. What is the expected number of occurrences of the pattern 'az+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, e: 5, a: 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": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 5, b: 2, w: 1, c: 1}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 1, u: 1, s: 2, m: 2, v: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, f: 3, m: 3}, what is the expected number of times the pattern 'm.*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": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 5, s: 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": "0.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 3, d: 1, u: 4} to form a word, what is the expected number of matches of the pattern 'uj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, z: 1, f: 3, d: 2, p: 1}. What is the expected number of occurrences of the pattern 'z.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, v: 4, e: 4, n: 2}, what is the expected number of times the pattern 't*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, q: 2, h: 1, g: 3}. What is the expected number of occurrences of the pattern 'qh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.06", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, o: 5, k: 2} to form a word, what is the expected number of matches of the pattern 'o*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": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, m: 2, o: 6}, 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": "0.72", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 8, d: 4}, what is the expected number of times the pattern 'z.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 1, u: 3, z: 1, l: 4}, 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": "2.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 5, o: 5}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, z: 2, o: 2, w: 1, s: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, d: 4, s: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'sw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, j: 6} to form a word, what is the expected number of matches of the pattern 'jb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 5, o: 4} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, q: 4} to form a word, what is the expected number of matches of the pattern 'q.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.86", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, o: 3, b: 3, p: 1, u: 2}, what is the expected number of times the pattern 'up*' 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 3 letters from the multiset {k: 1, p: 2, n: 4, o: 3, y: 1} 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 5, c: 1, g: 4}, what is the expected number of times the pattern 'g+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 6, l: 4}, what is the expected number of times the pattern 'kl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, n: 6, k: 2}, what is the expected number of times the pattern 'n*k' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, x: 3, i: 7}, what is the expected number of times the pattern 'gi*' 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": "Form a word by randomly choosing 3 letters from the multiset {h: 1, j: 1, c: 4, w: 2, o: 2}. What is the expected number of occurrences of the pattern 'h+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": "0.04", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 11, a: 1}. What is the expected number of occurrences of the pattern 'd*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": "0.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, b: 1, a: 1, g: 4, p: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, p: 4} 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": "0.86", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 7, 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": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, o: 1, x: 3, w: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, d: 2, q: 2, o: 3, p: 2}. What is the expected number of occurrences of the pattern 'o*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 5, r: 4}, what is the expected number of times the pattern 'kr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 1, z: 4, l: 1, u: 3, q: 3}, what is the expected number of times the pattern 'yq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 6, p: 5}. What is the expected number of occurrences of the pattern 'lp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, j: 5, f: 1, p: 2}, what is the expected number of times the pattern 'c+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 6, n: 4} to form a word, what is the expected number of matches of the pattern 'ni*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, m: 7} to form a word, what is the expected number of matches of the pattern 'gm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, j: 3, p: 5}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, y: 2, z: 1, a: 5} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, w: 3, h: 3, z: 1}, what is the expected number of times the pattern 'zw+' 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 4 letters from the multiset {t: 1, n: 4, m: 1, s: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, w: 2, g: 4, z: 2}. What is the expected number of occurrences of the pattern 'w+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, g: 5, n: 3}. What is the expected number of occurrences of the pattern 'n*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 2, v: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, o: 6}. What is the expected number of occurrences of the pattern 'o.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, h: 4, u: 4} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, y: 2, z: 2, a: 1, r: 1}. What is the expected number of occurrences of the pattern 'aa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, x: 1, g: 4, t: 4} to form a word, what is the expected number of matches of the pattern 'gx*'? 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 3 letters from the multiset {v: 6, m: 3}. What is the expected number of occurrences of the pattern 'v+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, t: 3, l: 2, g: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, j: 2, g: 4}. What is the expected number of occurrences of the pattern 'g*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.62", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, v: 2, d: 2, a: 1, g: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 3, u: 2, z: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'z.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 4, g: 3, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, o: 1, p: 1, s: 2, n: 2}. What is the expected number of occurrences of the pattern 'sn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, i: 2, h: 3, x: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'h+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, p: 2, c: 5}. What is the expected number of occurrences of the pattern 'c+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.42", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, q: 1, k: 2, y: 2, 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": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, z: 1, r: 1, n: 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": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 6, f: 1, v: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, m: 1, c: 1, z: 3, g: 1}, what is the expected number of times the pattern 'm.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, p: 6}, what is the expected number of times the pattern 'p.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, v: 1, m: 1, n: 2, p: 3} 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": "0.12", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 7, c: 5}. 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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 3, l: 9}. What is the expected number of occurrences of the pattern 'h.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 3, s: 1, c: 4, j: 4} to form a word, what is the expected number of matches of the pattern 'kc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 2, b: 2, t: 3, i: 4}, what is the expected number of times the pattern 'yd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 4, y: 5, g: 3}, what is the expected number of times the pattern 'gy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, z: 3, y: 5}. What is the expected number of occurrences of the pattern 'z*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, o: 1, f: 4, y: 4} to form a word, what is the expected number of matches of the pattern 'f*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.72", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, e: 1, p: 1, k: 4, s: 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": "0.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, r: 3, t: 2, o: 1}. 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, m: 1, o: 1, q: 2}. What is the expected number of occurrences of the pattern 'o*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": "0.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 5, e: 1, p: 3}. What is the expected number of occurrences of the pattern 'sp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 2, p: 3, x: 1, j: 2, i: 4}. What is the expected number of occurrences of the pattern 'v.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, y: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'ld+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, k: 1, f: 5}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, o: 2, b: 6}, 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": "1.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 5, u: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'u*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 4, a: 2, z: 3} to form a word, what is the expected number of matches of the pattern 'al*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, l: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'y+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 5, f: 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 5, 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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 3, e: 3, t: 2, q: 3, d: 1}, 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": "0.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 5, l: 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": "0.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, j: 2, o: 3}, what is the expected number of times the pattern 'j+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 5, o: 4}, 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": "2.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 3, b: 5}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, b: 2, v: 4, g: 3}. What is the expected number of occurrences of the pattern 'g*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": "0.92", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, o: 3, y: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'y+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 6, r: 3}. What is the expected number of occurrences of the pattern 'j.*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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 6, n: 1, q: 3, r: 2}, what is the expected number of times the pattern 'n+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, x: 6} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 1, n: 2, v: 2, y: 2, e: 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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 5, e: 4}. What is the expected number of occurrences of the pattern 'ae*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.34", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, s: 5}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, w: 2, l: 3, n: 1, e: 3}. What is the expected number of occurrences of the pattern 'we*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, m: 5}, what is the expected number of times the pattern 'ym+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 4, e: 6} 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": "1.03", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, n: 1, e: 2, k: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, z: 4, a: 2, l: 1}, what is the expected number of times the pattern 'z.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, t: 2, q: 2, c: 5, k: 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": "0.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, s: 3, i: 3, o: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 5, m: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, f: 3, q: 6, c: 1}, what is the expected number of times the pattern 'cp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.38", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 7, a: 5}, what is the expected number of times the pattern 'ao+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 2, t: 2, g: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'ta*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, r: 4, f: 1, x: 3}, what is the expected number of times the pattern 'a*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, c: 3, g: 5, d: 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 2, x: 6} to form a word, what is the expected number of matches of the pattern 'xn+'? 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 3 letters from the multiset {k: 6, d: 3}. What is the expected number of occurrences of the pattern 'kd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 6, c: 2}. What is the expected number of occurrences of the pattern 'c*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, b: 1, l: 3, x: 2}, what is the expected number of times the pattern 'cl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, r: 2, o: 5}. 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": "0.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, r: 1, k: 4, t: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, p: 2, i: 5}. What is the expected number of occurrences of the pattern 'p*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": "1.42", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, u: 3, d: 4, b: 2}, what is the expected number of times the pattern 'd.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, g: 1, z: 2, e: 4, x: 1}, what is the expected number of times the pattern 'ez*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, p: 3, o: 5} to form a word, what is the expected number of matches of the pattern 'po*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, t: 3, n: 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": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, y: 3, z: 3}. What is the expected number of occurrences of the pattern 'z.*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": "0.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, d: 3, e: 2, n: 2}. What is the expected number of occurrences of the pattern 'e.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, u: 3, l: 1, c: 1, e: 1}, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 1, b: 4, n: 1, a: 3, k: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 6, x: 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, b: 2, v: 4, s: 4}. 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": "0.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, h: 2, q: 3, e: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, j: 3, h: 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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, s: 3, d: 4}. 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, w: 2, i: 3, t: 3}, what is the expected number of times the pattern 'wt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, r: 1, i: 4, v: 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": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 9, q: 3}, what is the expected number of times the pattern 'q+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 1, d: 2, b: 1, x: 3, k: 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": "0.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 1, h: 3, g: 5} to form a word, what is the expected number of matches of the pattern 'vh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 6, w: 5}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 7, i: 4}, what is the expected number of times the pattern 'r+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, h: 2, o: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'e*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, p: 1, z: 3, e: 1, s: 1}. What is the expected number of occurrences of the pattern 'p+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": "0.05", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, w: 2, n: 1, s: 3, v: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, b: 2, j: 4, a: 2}, what is the expected number of times the pattern 'ja*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, x: 1, d: 1, k: 4, g: 3}, what is the expected number of times the pattern 'k.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, s: 6}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, b: 2, n: 2, q: 5}. What is the expected number of occurrences of the pattern 'vq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, w: 2, p: 2, k: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'k+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 1, i: 3, z: 2, x: 4, w: 2}. What is the expected number of occurrences of the pattern 'xa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.42", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, d: 7} to form a word, what is the expected number of matches of the pattern 'd.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, y: 2, f: 1, g: 2, z: 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 3, w: 2, o: 2}, 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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, p: 2, g: 2, a: 2, j: 1}, what is the expected number of times the pattern 'ap+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, j: 2, a: 4, c: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, r: 3, h: 2, i: 5}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, y: 2, i: 3}. What is the expected number of occurrences of the pattern 'yi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, n: 6} 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, s: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'as*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 5, u: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'y.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, j: 4, c: 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, x: 2, q: 2, b: 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": "0.06", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, f: 3, e: 1, v: 1, z: 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": "1.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, e: 4, i: 2, x: 1, n: 2}. What is the expected number of occurrences of the pattern 'i*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": "1.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 1, j: 2, l: 1, t: 3, m: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, y: 1, l: 4, c: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, c: 1, t: 3, z: 2, j: 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, t: 1, c: 5, j: 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": "0.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 4, l: 4} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, b: 2, d: 3, u: 4, m: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, x: 3, m: 2, h: 2, n: 2}, what is the expected number of times the pattern 'hj+' 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 3 by randomly selecting letters from the multiset {p: 3, r: 2, y: 2, x: 1, g: 2}, what is the expected number of times the pattern 'g+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, n: 2, w: 3, i: 1, e: 2}, what is the expected number of times the pattern 'w.*n' 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 4 letters from the multiset {q: 4, b: 1, h: 1, j: 4}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, t: 6}, what is the expected number of times the pattern 't+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.61", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 4, v: 1, r: 6}. 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": "Form a word by randomly choosing 3 letters from the multiset {y: 3, f: 2, l: 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": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, s: 3, o: 2, m: 1, x: 1}. What is the expected number of occurrences of the pattern 'xs*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 7, a: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, l: 2, z: 2, p: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'j*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 5, s: 3, u: 1, n: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'nf*'? 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 4 by randomly selecting letters from the multiset {l: 5, w: 5}, what is the expected number of times the pattern 'wl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 2, a: 5, p: 2}, what is the expected number of times the pattern 'w+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, o: 5}, 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": "1.84", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, h: 8}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, d: 2, w: 3, f: 2, c: 4}, what is the expected number of times the pattern 'w.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, t: 2, q: 1, v: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'q+t'? 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 4 letters from the multiset {p: 3, l: 2, q: 2, b: 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": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, z: 3, q: 3, b: 2}. What is the expected number of occurrences of the pattern 'k+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, f: 1, w: 3, p: 1}. What is the expected number of occurrences of the pattern 'pw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, d: 3, a: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 5, s: 1, d: 3, m: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, u: 2, o: 3}. What is the expected number of occurrences of the pattern 'u*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, e: 6}. 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": "0.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, n: 2, k: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 7, f: 3}. What is the expected number of occurrences of the pattern 'fp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, e: 4, z: 3, n: 2}. What is the expected number of occurrences of the pattern 'zn+' in 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 4 by randomly selecting letters from the multiset {a: 5, w: 4, n: 3}, what is the expected number of times the pattern 'n+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.31", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 1, n: 1, o: 2, i: 2, k: 2}. What is the expected number of occurrences of the pattern 'oi+' in 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 3 letters from the multiset {r: 2, z: 2, t: 1, o: 1, m: 2}. What is the expected number of occurrences of the pattern 'r.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 3, w: 1, u: 3, y: 1}. What is the expected number of occurrences of the pattern 'h+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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 2, n: 2, o: 2, x: 2}, what is the expected number of times the pattern 'n*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, e: 6} to form a word, what is the expected number of matches of the pattern 's+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 2, f: 2, h: 1, p: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'h+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, a: 5, f: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'j+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 5, p: 3, j: 1, y: 2, d: 1}, what is the expected number of times the pattern 'y.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, t: 4, h: 4}, what is the expected number of times the pattern 't*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 1, v: 1, k: 3, r: 1, o: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, v: 4, x: 2, a: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, b: 2, t: 4, p: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 3, f: 4, 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 6, k: 5} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, e: 3, z: 5}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, v: 2, p: 1, y: 2, j: 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": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 2, i: 4, c: 4}. What is the expected number of occurrences of the pattern 'vc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, u: 3, q: 3}, what is the expected number of times the pattern 'u*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 1, t: 2, s: 2, a: 2, r: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, v: 2, o: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, s: 4}. What is the expected number of occurrences of the pattern 'se*' 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 4 by randomly selecting letters from the multiset {f: 5, u: 1, b: 2}, what is the expected number of times the pattern 'f*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.85", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 2, e: 2, f: 1, s: 2, j: 3} 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": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, t: 3, x: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'x+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, e: 5, a: 3}, 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": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, k: 1, s: 1, p: 3, c: 1}, what is the expected number of times the pattern 'ck+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 1, n: 4, x: 1, a: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, d: 4, u: 2, l: 2, h: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, w: 7}. What is the expected number of occurrences of the pattern 'w*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": "2.66", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, o: 2, k: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'g*o'? 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 3 letters from the multiset {n: 4, s: 7}. 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, l: 2, r: 1, k: 2, b: 1}. What is the expected number of occurrences of the pattern 'kr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.72", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, a: 1, w: 2, o: 3, l: 2} 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": "0.72", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, e: 3, y: 2, g: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, r: 2, w: 4, h: 2}. What is the expected number of occurrences of the pattern 'hi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, e: 1, u: 1, k: 2, i: 3}, what is the expected number of times the pattern 'k*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 1, u: 2, m: 2, p: 4, a: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, f: 5}, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 1, w: 7, g: 3} to form a word, what is the expected number of matches of the pattern 'y+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, s: 8}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, y: 2, c: 2, f: 3, a: 3}. What is the expected number of occurrences of the pattern 'f*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, y: 3, l: 1, p: 1}, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 5, r: 1, m: 3} to form a word, what is the expected number of matches of the pattern 's.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 6, b: 6}, what is the expected number of times the pattern 'qb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 7, h: 1, d: 2, v: 1, p: 1}, 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": "Form a word by randomly choosing 4 letters from the multiset {t: 3, y: 5}. What is the expected number of occurrences of the pattern 'y.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, u: 4, q: 2, y: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 1, r: 5, w: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'r.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 4, q: 3, u: 2}. What is the expected number of occurrences of the pattern 'qe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, k: 1, p: 2, s: 2, y: 4}. What is the expected number of occurrences of the pattern 's+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 1, g: 1, u: 3, k: 4, 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": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, g: 3, s: 3, e: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 3, c: 1, p: 5} 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": "2.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, c: 4}. What is the expected number of occurrences of the pattern 'nc*' 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 3 by randomly selecting letters from the multiset {c: 2, n: 3, k: 3, i: 2, o: 2}, what is the expected number of times the pattern 'k+c' 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 4 by randomly selecting letters from the multiset {a: 2, c: 2, z: 3, w: 3}, what is the expected number of times the pattern 'ac*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 6, d: 4}, what is the expected number of times the pattern 'hd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.43", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, t: 2, c: 3, l: 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": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, x: 1, s: 1, a: 3, m: 2}, what is the expected number of times the pattern 's*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 5, g: 2, l: 5}. What is the expected number of occurrences of the pattern 'l.*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": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 5, j: 2, d: 3}. What is the expected number of occurrences of the pattern 'a+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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 6, j: 1, p: 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": "0.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, d: 3, x: 3, b: 1, a: 1}, what is the expected number of times the pattern 'av*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 1, x: 3, p: 5, r: 3} to form a word, what is the expected number of matches of the pattern 'ix+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 7, a: 4}, what is the expected number of times the pattern 'h+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, d: 1, w: 4, j: 3}, what is the expected number of times the pattern 'j*i' 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 {f: 3, h: 2, y: 5, r: 2}. What is the expected number of occurrences of the pattern 'yf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, e: 2, w: 2, l: 4}, what is the expected number of times the pattern 'r.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 5, y: 5}. What is the expected number of occurrences of the pattern 'y*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": "4.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 6, g: 4, z: 1}. What is the expected number of occurrences of the pattern 'z+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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 3, w: 2, y: 2, z: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'y*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.42", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 6, k: 8}, what is the expected number of times the pattern 'ki+' 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": "When randomly selecting 4 letters from the multiset {v: 2, a: 7, g: 3} to form a word, what is the expected number of matches of the pattern 'va*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 4, d: 2, r: 3, h: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 5, x: 5, d: 1, s: 2}. What is the expected number of occurrences of the pattern 'x+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 6, f: 3, c: 4, d: 1}, what is the expected number of times the pattern 'q*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 2, g: 2, h: 3, f: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 1, k: 7, d: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 5, h: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'fr+'? 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 {d: 2, a: 3, x: 4, i: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.26", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 4, c: 6} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 4, o: 6} to form a word, what is the expected number of matches of the pattern 'ox*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, o: 2, k: 4, w: 1}. What is the expected number of occurrences of the pattern 'w+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, q: 5, u: 4}, 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": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 4, g: 1, f: 1, x: 5}, what is the expected number of times the pattern 'x*f' 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 4 letters from the multiset {q: 3, y: 8, p: 4} to form a word, what is the expected number of matches of the pattern 'qp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 2, l: 2, t: 6, c: 2} to form a word, what is the expected number of matches of the pattern 'lt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.05", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 3, m: 3, x: 2, z: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'xo+'? 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 {u: 1, m: 3, f: 2, e: 3, g: 4}. 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": "0.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 4, p: 4, t: 5}. What is the expected number of occurrences of the pattern 'n+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 4, j: 3, k: 1, w: 3, r: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 4, o: 1, u: 6} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 5, k: 4, f: 4} to form a word, what is the expected number of matches of the pattern 'ik+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 1, g: 4, a: 3, o: 1, d: 2}, what is the expected number of times the pattern 'k.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, b: 5, u: 4}. What is the expected number of occurrences of the pattern 'u+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.31", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 3, p: 4, n: 6, k: 1}. What is the expected number of occurrences of the pattern 'kp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 2, r: 9} to form a word, what is the expected number of matches of the pattern 'r*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 5, m: 6}. What is the expected number of occurrences of the pattern 'md+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 8, b: 6} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.99", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, e: 5, i: 8}. 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": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 2, s: 2, g: 4, o: 1, q: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, z: 2, r: 3, e: 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 5, t: 6}, 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 1, c: 6, o: 4, w: 1} 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": "0.05", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 11, d: 3}, what is the expected number of times the pattern 'a*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 9, f: 6}. What is the expected number of occurrences of the pattern 'fq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, p: 7, q: 4}. What is the expected number of occurrences of the pattern 'p+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 6, f: 6}. What is the expected number of occurrences of the pattern 'c.*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": "1.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 5, y: 1, s: 2, j: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 3, o: 4, a: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, l: 3, p: 4, t: 2, b: 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": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 3, p: 2, o: 4, m: 5} to form a word, what is the expected number of matches of the pattern 'eo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {u: 3, y: 5, h: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 4, l: 3, j: 3, u: 2}. 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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 3, a: 2, m: 5} 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 7, i: 8}. What is the expected number of occurrences of the pattern 'i*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.03", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 9, m: 6}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 4, c: 3, x: 1, d: 4, b: 2}. What is the expected number of occurrences of the pattern 'cb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, j: 1, g: 2, f: 3, s: 2}, what is the expected number of times the pattern 'f.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 4, c: 2, j: 2, y: 3, q: 3}, 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": "1.62", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, d: 5}, what is the expected number of times the pattern 'd*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, m: 4, f: 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": "2.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, k: 1, p: 3, g: 4, l: 1}, what is the expected number of times the pattern 'pl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 4, i: 5, y: 3} 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": "0.55", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 7, u: 1, a: 4, f: 3} to form a word, what is the expected number of matches of the pattern 'eu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 6, l: 5, y: 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 6, p: 1, a: 4, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, i: 4, j: 3, k: 2}, what is the expected number of times the pattern 'ki+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.31", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 2, o: 4, b: 2, u: 2, d: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, u: 2, n: 2, e: 1, w: 4}, what is the expected number of times the pattern 'e.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, b: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 6, k: 8}. What is the expected number of occurrences of the pattern 'z+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": "Form a word by randomly choosing 5 letters from the multiset {x: 2, u: 8, v: 4}. What is the expected number of occurrences of the pattern 'uv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.71", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 4, l: 3, w: 4}, what is the expected number of times the pattern 'gw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 2, d: 4, a: 3, y: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, z: 5, w: 1}, what is the expected number of times the pattern 'z*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 5, z: 4, h: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'z.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, y: 6, j: 2, p: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 5, n: 4, t: 6} to form a word, what is the expected number of matches of the pattern 'gn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.12", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 4, q: 1, n: 6, c: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 3, t: 7} to form a word, what is the expected number of matches of the pattern 'tr*'? 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 {q: 3, s: 3, j: 2, p: 3, i: 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 3, w: 4, u: 3, p: 2}, what is the expected number of times the pattern 'u*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 5, v: 6}, what is the expected number of times the pattern 'v+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 5, f: 3, x: 2, y: 1, 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 2, f: 8, t: 1, o: 1, e: 2}. What is the expected number of occurrences of the pattern 'f*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, h: 3, o: 2, k: 2, s: 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 2, n: 2, x: 5, k: 3, r: 1}. What is the expected number of occurrences of the pattern 'q+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 6, u: 6, x: 3}. What is the expected number of occurrences of the pattern 'u*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": "1.47", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 3, k: 2, b: 3, t: 1, s: 2}. What is the expected number of occurrences of the pattern 's+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 4, g: 2, v: 4, k: 4}, what is the expected number of times the pattern 'a.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 1, p: 5, g: 6} to form a word, what is the expected number of matches of the pattern 'py*'? 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": "When randomly selecting 5 letters from the multiset {s: 1, c: 6, o: 4, x: 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": "1.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 6, q: 4, k: 4}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 5, i: 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": "Form a word by randomly choosing 4 letters from the multiset {j: 3, z: 3, r: 3, a: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 4, v: 2, j: 6} to form a word, what is the expected number of matches of the pattern 'l*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.42", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 4, r: 2, q: 5, 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": "0.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, f: 5, v: 2, d: 5}, what is the expected number of times the pattern 'df+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.61", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 7, x: 2, b: 2}, what is the expected number of times the pattern 'yx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, p: 3, t: 1, l: 4} 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 1, x: 1, q: 1, h: 4, z: 3}. 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 3, w: 4, a: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 7, o: 4}, 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 3, e: 3, o: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'e+t'? 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, t: 2, z: 1, r: 4, f: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, x: 5, j: 3}. What is the expected number of occurrences of the pattern 'zj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 2, t: 4, h: 1, r: 7}, what is the expected number of times the pattern 't+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 4, k: 5, l: 6}. What is the expected number of occurrences of the pattern 'lk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 3, x: 4, z: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 7, f: 2, u: 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 7, m: 5} to form a word, what is the expected number of matches of the pattern 'm+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 6, h: 4, v: 2, q: 1}. What is the expected number of occurrences of the pattern 'q.*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": "0.26", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 6, h: 4}. What is the expected number of occurrences of the pattern 'w*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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 3, o: 3, b: 6, q: 1, l: 2}. What is the expected number of occurrences of the pattern 'lb+' in 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 {f: 2, q: 1, b: 2, i: 4, p: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 4, n: 11} 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": "2.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 4, g: 1, i: 3, a: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'i*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.42", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {v: 4, s: 2, u: 2, g: 4} 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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 7, u: 4, 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": "2.31", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 5, h: 7} 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": "1.04", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 4, g: 5, n: 3} to form a word, what is the expected number of matches of the pattern 'x*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": "Form a word by randomly choosing 4 letters from the multiset {i: 4, w: 4, y: 1, g: 5}. What is the expected number of occurrences of the pattern 'iy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 3, e: 1, p: 3, o: 3, n: 1} to form a word, what is the expected number of matches of the pattern 's+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.28", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 1, p: 6, r: 4} to form a word, what is the expected number of matches of the pattern 'pb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.35", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 1, w: 2, a: 3, q: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'qw+'? 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 {r: 2, i: 2, u: 6, p: 4}, what is the expected number of times the pattern 'i+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 2, e: 3, a: 4, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 3, r: 7}, what is the expected number of times the pattern 'lr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 2, q: 3, p: 1, h: 4} to form a word, what is the expected number of matches of the pattern 'i.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 6, t: 1, z: 3, j: 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": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 8, q: 6}, what is the expected number of times the pattern 'v*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, m: 4, d: 5, n: 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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 3, d: 4, w: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 2, i: 2, p: 5, f: 4, z: 2}, what is the expected number of times the pattern 'p*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, u: 5, r: 4, j: 3}, what is the expected number of times the pattern 'j*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.94", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, y: 9}, what is the expected number of times the pattern 't.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, g: 2, t: 1, k: 2, m: 4} 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": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, s: 2, p: 3, i: 3, l: 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": "0.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, h: 5, k: 5}, what is the expected number of times the pattern 'kh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.94", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 1, i: 3, e: 3, s: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'p.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, w: 3, p: 4, o: 1, j: 1}. What is the expected number of occurrences of the pattern 'pj+' in 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 {j: 7, a: 8} 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": "2.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 6, u: 4} to form a word, what is the expected number of matches of the pattern 'uq+'? 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 {m: 3, v: 3, d: 3, x: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'ov*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 11, v: 3}. What is the expected number of occurrences of the pattern 'v*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 4, p: 4, g: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'p*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.85", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 6, b: 2, u: 4, a: 2}, what is the expected number of times the pattern 'ww+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, f: 7, a: 5} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, w: 2, x: 2, g: 4}, what is the expected number of times the pattern 'w*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 7, e: 5}, 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": "1.76", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 4, j: 3, q: 4} to form a word, what is the expected number of matches of the pattern 'q.*j'? 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 4 letters from the multiset {u: 2, n: 4, a: 2, c: 1, b: 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 5, y: 5, n: 4}, what is the expected number of times the pattern 'y.*n' 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 4 letters from the multiset {g: 7, j: 6}. What is the expected number of occurrences of the pattern 'j+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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 3, g: 11} 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {t: 7, o: 2, h: 5} to form a word, what is the expected number of matches of the pattern 'oh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, f: 4, e: 4}, what is the expected number of times the pattern 'ef*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 6, d: 5}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, e: 3, c: 4, 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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 2, a: 2, v: 2, c: 1, k: 4} to form a word, what is the expected number of matches of the pattern 'kb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 3, c: 2, a: 3, q: 6} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 4, l: 4, u: 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, p: 1, x: 3, o: 2, s: 1}, what is the expected number of times the pattern 'e.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 2, r: 5, h: 1, u: 3, g: 3}, what is the expected number of times the pattern 'u+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 4, m: 3, u: 4} to form a word, what is the expected number of matches of the pattern 'du+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, g: 3, f: 3, i: 1, n: 3}, what is the expected number of times the pattern 'f+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 6, p: 5, a: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 3, x: 5, e: 3} to form a word, what is the expected number of matches of the pattern 'c.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, f: 1, l: 2, e: 2, c: 3}. What is the expected number of occurrences of the pattern 'cr+' in 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 {t: 4, n: 2, e: 2, z: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'zt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 7, d: 3, z: 2, r: 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": "0.41", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, y: 4, b: 6}, what is the expected number of times the pattern 'yv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, b: 6, l: 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": "2.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 4, f: 2, g: 1, t: 3, z: 4}, what is the expected number of times the pattern 'fk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 2, g: 4, s: 2, a: 2, n: 4}. What is the expected number of occurrences of the pattern 'g.*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": "0.26", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 5, g: 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": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 3, d: 1, e: 3, f: 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": "0.41", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 6, b: 3, s: 5}. What is the expected number of occurrences of the pattern 'vb+' in 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 {s: 3, w: 3, j: 4}. What is the expected number of occurrences of the pattern 'w.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, p: 3, y: 2, u: 4}, what is the expected number of times the pattern 'yu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 7, o: 7}, what is the expected number of times the pattern 'yo+' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, p: 4, l: 3, j: 1}, what is the expected number of times the pattern 'jl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, a: 2, y: 2, p: 5, k: 2}. What is the expected number of occurrences of the pattern 'yk+' in 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 {j: 5, k: 6, o: 4}, what is the expected number of times the pattern 'jo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 3, q: 4, z: 5} to form a word, what is the expected number of matches of the pattern 'nq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 2, s: 2, l: 4, y: 2}. What is the expected number of occurrences of the pattern 'sy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 5, i: 3, x: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, h: 2, r: 4, w: 2}, what is the expected number of times the pattern 'wl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 3, o: 2, c: 5, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 9, n: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 2, l: 2, k: 3, r: 3, f: 1} 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": "0.55", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 5, g: 6, o: 4}, what is the expected number of times the pattern 'oc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.35", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 4, c: 3, b: 3, a: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 4, k: 1, z: 4, q: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {o: 3, e: 3, v: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'v+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 6, o: 6} to form a word, what is the expected number of matches of the pattern 'ov+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 6, c: 5, i: 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, j: 6, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 3, g: 5, j: 2} to form a word, what is the expected number of matches of the pattern 'q+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 5, r: 7} to form a word, what is the expected number of matches of the pattern 'hr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, p: 2, g: 4, i: 5}, what is the expected number of times the pattern 'i*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.86", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 2, r: 4, s: 2, f: 2}. 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": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 1, e: 5, f: 2, n: 3}. What is the expected number of occurrences of the pattern 'n*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.92", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 10, h: 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": "5.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 6, c: 4} to form a word, what is the expected number of matches of the pattern 'p*c'? 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: 1, n: 3, x: 3, z: 1, p: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 4, q: 4, b: 6}. 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": "2.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 5, d: 4, t: 5}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 5, p: 5, i: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, o: 4, u: 5}, what is the expected number of times the pattern 'o+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, z: 3, d: 4, v: 2}, what is the expected number of times the pattern 'z*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, f: 2, i: 3, v: 4, b: 3}, what is the expected number of times the pattern 'f+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, b: 3, g: 6, r: 3, t: 2}. What is the expected number of occurrences of the pattern 'g.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {p: 4, l: 3, h: 1, z: 2, r: 2}. What is the expected number of occurrences of the pattern 'z*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.96", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, y: 1, f: 7, n: 2, u: 2}, what is the expected number of times the pattern 'nv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, k: 4, i: 3, x: 2, b: 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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 2, i: 4, v: 2, o: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'j.*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": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 8, h: 6}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.85", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, s: 2, p: 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": "1.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 4, n: 1, o: 1, e: 3, c: 5} to form a word, what is the expected number of matches of the pattern 'k+n'? 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: 3, r: 5, j: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 8, d: 4} to form a word, what is the expected number of matches of the pattern 'fd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.56", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 3, s: 3, u: 2, f: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'g*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 4, d: 6} to form a word, what is the expected number of matches of the pattern 'jd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 4, f: 2, p: 2, s: 1, j: 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 7, v: 3}. What is the expected number of occurrences of the pattern 'z*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 2, h: 2, z: 5, o: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'o+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 4, n: 4, e: 4, j: 2}. 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": "0.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, w: 3, x: 4, e: 2}, 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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 4, p: 3, f: 2, v: 3}. What is the expected number of occurrences of the pattern 'av*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 6, 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": "1.85", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 1, c: 4, r: 3, y: 3}. 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 {v: 8, y: 6}, 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": "1.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 7, i: 6}, what is the expected number of times the pattern 'i*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.26", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 5, c: 4, a: 1, e: 4}, what is the expected number of times the pattern 'y*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.56", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, z: 7}, what is the expected number of times the pattern 'z+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 1, t: 2, p: 3, w: 4, j: 4}, what is the expected number of times the pattern 'w+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 6, u: 3, t: 2, x: 1, i: 2}, what is the expected number of times the pattern 'w+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, m: 2, a: 1, c: 2, v: 6}. What is the expected number of occurrences of the pattern 'a*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": "1.96", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 2, u: 4, a: 2, h: 4}, what is the expected number of times the pattern 't*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.96", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 4, n: 5, q: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'q*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.28", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 8, z: 4}. What is the expected number of occurrences of the pattern 'z+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": "1.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 5, o: 7, t: 3} to form a word, what is the expected number of matches of the pattern 'n.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, h: 2, n: 3}. What is the expected number of occurrences of the pattern 'nl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 6, l: 4} to form a word, what is the expected number of matches of the pattern 'sl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.43", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 1, e: 5, a: 4, x: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'e+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 9, z: 4}. 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": "0.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 4, l: 5, m: 5} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, k: 3, z: 2, g: 3, r: 2}, what is the expected number of times the pattern 'gr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, r: 2, g: 3, z: 4, n: 2}, what is the expected number of times the pattern 'zd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 5, f: 2, i: 2, o: 3, g: 2}. What is the expected number of occurrences of the pattern 'a.*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": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, f: 6}, 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": "4.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, z: 6, o: 2, t: 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": "0.86", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 6, b: 4, d: 4} to form a word, what is the expected number of matches of the pattern 'n*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 5, b: 6}. What is the expected number of occurrences of the pattern 'gg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.21", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 6, h: 7}, what is the expected number of times the pattern 'ht*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 4, t: 2, k: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'm*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 4, h: 7} to form a word, what is the expected number of matches of the pattern 'h.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 3, y: 3, g: 6}. What is the expected number of occurrences of the pattern 'g*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.58", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, a: 1, c: 3, m: 4, o: 4}, what is the expected number of times the pattern 'm.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, s: 2, l: 1, m: 5, c: 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": "0.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, i: 2, o: 3, b: 4, w: 1}, what is the expected number of times the pattern 'wi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, h: 4, f: 3, m: 2, s: 5}. What is the expected number of occurrences of the pattern 'h*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 8, t: 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": "0.31", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, a: 3, i: 3, v: 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": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, e: 2, a: 4, q: 4, h: 2}, what is the expected number of times the pattern 'q*e' 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 {s: 5, o: 6} to form a word, what is the expected number of matches of the pattern 'so+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 4, e: 4, w: 2, c: 2, f: 1}, what is the expected number of times the pattern 'c*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.39", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {j: 3, e: 4, r: 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 7, h: 5}, what is the expected number of times the pattern 'wh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 4, f: 2, p: 4, a: 1}. 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": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, o: 8}, 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": "5.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 7, v: 7} to form a word, what is the expected number of matches of the pattern 'v*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.14", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 7, s: 4, y: 3} 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, v: 1, e: 3, a: 3, d: 2}. What is the expected number of occurrences of the pattern 'ed*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.42", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 7, o: 7}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.38", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 5, d: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'e+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 5, t: 4, v: 2}. What is the expected number of occurrences of the pattern 'tv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 7, v: 5}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, p: 3, d: 3}, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 7, r: 5}, what is the expected number of times the pattern 'r.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.59", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, v: 2, f: 4, m: 2, k: 2}. What is the expected number of occurrences of the pattern 'mv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 6, i: 6}, what is the expected number of times the pattern 'mi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 6, r: 5}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 6, r: 3, j: 4}, what is the expected number of times the pattern 'r*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.24", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 4, i: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 3, r: 3, y: 4, b: 1}, what is the expected number of times the pattern 'lr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 6, e: 5, b: 4}. 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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 6, p: 5}. What is the expected number of occurrences of the pattern 'k.*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": "1.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 7, f: 4} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 1, t: 2, z: 5, q: 5}, what is the expected number of times the pattern 'q+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 8, w: 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": "2.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 5, i: 4, y: 6} to form a word, what is the expected number of matches of the pattern 'iy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.51", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 10, f: 5} 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": "2.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, q: 3, f: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 9, x: 3}, what is the expected number of times the pattern 't.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.05", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 3, c: 3, v: 3, e: 3, y: 2} to form a word, what is the expected number of matches of the pattern 've+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 4, e: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 2, x: 2, f: 4, s: 4, a: 3}, 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": "0.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 4, q: 3, j: 5} to form a word, what is the expected number of matches of the pattern 'yj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 3, l: 3, f: 5, u: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 6, x: 5}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 5, v: 3, f: 3, n: 3}, what is the expected number of times the pattern 'fn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 7, n: 4, y: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 6, b: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 3, x: 4, b: 7}. What is the expected number of occurrences of the pattern 'qq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.96", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 7, d: 5}. What is the expected number of occurrences of the pattern 'o+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.76", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, p: 8, l: 3} to form a word, what is the expected number of matches of the pattern 'hl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.26", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 4, z: 1, m: 5, l: 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": "0.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, u: 2, w: 1, r: 3, s: 2}. 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": "0.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 6, f: 5, m: 3}. What is the expected number of occurrences of the pattern 'f.*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": "0.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 1, x: 5, a: 2, u: 2, s: 2}. What is the expected number of occurrences of the pattern 'sx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 5, m: 2, l: 7} to form a word, what is the expected number of matches of the pattern 'ml*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 3, d: 3, g: 3, p: 1}, 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": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 6, k: 2, j: 4}. What is the expected number of occurrences of the pattern 'd+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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 3, c: 5, z: 2, m: 4}, what is the expected number of times the pattern 'z.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 6, d: 9}, what is the expected number of times the pattern 'q+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 3, m: 2, e: 4, t: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'j*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 1, f: 3, l: 3, h: 3, y: 2}. What is the expected number of occurrences of the pattern 'f.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 3, n: 7, h: 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": "2.69", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 3, m: 1, k: 3, e: 3, p: 1}, what is the expected number of times the pattern 'me+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 5, m: 3, p: 3}, what is the expected number of times the pattern 'mp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.38", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 1, z: 2, w: 5, r: 5} 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": "0.38", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 8, p: 7}, what is the expected number of times the pattern 'lp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 6, l: 5} to form a word, what is the expected number of matches of the pattern 'l.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 5, p: 7}. What is the expected number of occurrences of the pattern 'k+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": "1.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, b: 2, t: 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 4 letters from the multiset {d: 7, z: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.47", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, h: 2, o: 1, t: 2, q: 5}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 7, t: 6}, what is the expected number of times the pattern 't*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.26", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 6, n: 3, s: 2}, what is the expected number of times the pattern 's*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 7, h: 6}, what is the expected number of times the pattern 'h+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, n: 2, c: 5, u: 2}. What is the expected number of occurrences of the pattern 'n.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 9, g: 6}. 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": "1.54", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, w: 4, o: 2, q: 2, r: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, t: 5, y: 5}, what is the expected number of times the pattern 'tl+' 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": "Form a word by randomly choosing 5 letters from the multiset {f: 4, g: 3, x: 2, h: 4, t: 2}. 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": "Form a word by randomly choosing 5 letters from the multiset {u: 4, g: 9, f: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 6, f: 6}, what is the expected number of times the pattern 'w.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, t: 7, d: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 6, l: 9}. What is the expected number of occurrences of the pattern 'lp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, v: 5, f: 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": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 9, q: 6}. What is the expected number of occurrences of the pattern 'w+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": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, q: 2, e: 2, t: 7}. What is the expected number of occurrences of the pattern 'e*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.44", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, x: 4, g: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'x+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 2, u: 2, o: 3, q: 3, f: 2}. What is the expected number of occurrences of the pattern 'qw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 3, d: 2, t: 1, e: 6}. What is the expected number of occurrences of the pattern 'oe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.82", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 3, g: 4, q: 1, t: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'to+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, k: 4, w: 3, j: 4}, 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": "0.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 5, d: 3, x: 7}, 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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 4, k: 6, t: 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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 5, k: 3, w: 5, c: 2} to form a word, what is the expected number of matches of the pattern 'c+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, m: 1, k: 1, h: 2, p: 4}, what is the expected number of times the pattern 'm+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {r: 3, t: 5, a: 2}. What is the expected number of occurrences of the pattern 't*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 5, a: 7, h: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, n: 3, b: 1, p: 6}, what is the expected number of times the pattern 'p.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 3, t: 2, p: 1, k: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 4, h: 2, i: 1, c: 4} to form a word, what is the expected number of matches of the pattern 'i.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 4, c: 1, j: 5, e: 1, b: 3}, what is the expected number of times the pattern 'j+c' 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 4 by randomly selecting letters from the multiset {b: 7, w: 6}, what is the expected number of times the pattern 'ww*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 1, c: 3, p: 8} to form a word, what is the expected number of matches of the pattern 'ps+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 3, r: 4, s: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'r+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, b: 5, r: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 3, l: 4, z: 2, d: 2, h: 1}. What is the expected number of occurrences of the pattern 'zd+' in 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 {t: 3, k: 2, x: 3, v: 3}. 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": "0.39", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, c: 2, s: 5}, what is the expected number of times the pattern 'es+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 7, w: 4, k: 4}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 4, t: 7, p: 4}. What is the expected number of occurrences of the pattern 'p*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 4, c: 4, w: 2, o: 5}. What is the expected number of occurrences of the pattern 'c.*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": "0.76", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 7, f: 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": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, n: 4, l: 4} 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 8, f: 6}, 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": "3.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, m: 3, c: 5}. What is the expected number of occurrences of the pattern 'c*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 6, h: 5, s: 4}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 5, u: 6}. 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": "1.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, f: 4, t: 6}, what is the expected number of times the pattern 'tw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, v: 4, n: 2, m: 4}. What is the expected number of occurrences of the pattern 'v.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 4, q: 6}, what is the expected number of times the pattern 'f*q' 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": "Form a word by randomly choosing 4 letters from the multiset {k: 6, l: 3, d: 2}. 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": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 4, s: 4, g: 4}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 2, u: 4, h: 2, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 1, a: 2, q: 1, k: 2, x: 4}. What is the expected number of occurrences of the pattern 'hq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.43", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, m: 3, l: 5, v: 2}. 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": "0.91", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 3, x: 6, f: 5}. What is the expected number of occurrences of the pattern 'x.*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": "0.59", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 5, n: 6, s: 2} to form a word, what is the expected number of matches of the pattern 'ni*'? 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 {y: 2, q: 3, b: 3, u: 4}, what is the expected number of times the pattern 'ub+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.42", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 6, o: 6}. What is the expected number of occurrences of the pattern 'ot*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, a: 1, f: 3, n: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, z: 2, m: 4}, what is the expected number of times the pattern 'zt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, y: 2, l: 4, h: 3, e: 1}, 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": "0.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 4, b: 7, k: 1}, what is the expected number of times the pattern 'k+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 7, m: 8}, what is the expected number of times the pattern 'mp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 6, l: 6}. What is the expected number of occurrences of the pattern 'l.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 6, c: 3, x: 2, j: 3, m: 1}. What is the expected number of occurrences of the pattern 'x+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 6, c: 5} 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": "2.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 6, i: 6}, what is the expected number of times the pattern 'iy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 3, p: 6, j: 2} to form a word, what is the expected number of matches of the pattern 'j*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, v: 3, x: 2, b: 2, p: 3}, what is the expected number of times the pattern 'zp+' 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 4 letters from the multiset {x: 3, j: 4, r: 3, w: 1, b: 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {n: 1, t: 2, v: 3, z: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'z.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, a: 2, r: 3, s: 3}. 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": "0.35", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 9, q: 2, y: 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": "2.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 8, x: 7}, what is the expected number of times the pattern 'v.*x' 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 4 letters from the multiset {s: 2, d: 1, n: 1, p: 5, c: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 2, t: 4, e: 1, y: 5, b: 3} to form a word, what is the expected number of matches of the pattern 'ty+'? 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 {i: 4, s: 6, e: 5} 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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {z: 3, w: 4, x: 5, b: 3} to form a word, what is the expected number of matches of the pattern 'zb+'? 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 {u: 7, g: 4}. 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": "2.55", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, g: 1, o: 2, d: 3, y: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, y: 3, f: 2, i: 3}, what is the expected number of times the pattern 'y*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 4, r: 1, x: 2, e: 3}. 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": "0.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, p: 4, o: 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": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 2, j: 5, q: 4} to form a word, what is the expected number of matches of the pattern 'qs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.69", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 3, s: 3, z: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'e.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 4, n: 3, d: 4} to form a word, what is the expected number of matches of the pattern 'dp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 8, v: 6}. 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": "3.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 4, v: 3, b: 5, q: 1}. What is the expected number of occurrences of the pattern 'q*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": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 5, p: 2, h: 2, s: 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": "0.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 3, p: 7, d: 2, c: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'pi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, o: 4, u: 3, f: 5}, what is the expected number of times the pattern 'z.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 8, z: 5, c: 2}. What is the expected number of occurrences of the pattern 'c*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 7, o: 3} to form a word, what is the expected number of matches of the pattern 'i.*o'? 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 {g: 8, y: 3} to form a word, what is the expected number of matches of the pattern 'g+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 2, g: 3, n: 1, l: 5} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 7, p: 6}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.62", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, d: 4, z: 2, s: 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": "0.23", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 5, g: 2, m: 2, q: 3} to form a word, what is the expected number of matches of the pattern 't+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, e: 1, a: 2, c: 5, r: 4}, what is the expected number of times the pattern 'r*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 5, y: 5, p: 2, f: 2}. What is the expected number of occurrences of the pattern 'my+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {k: 1, z: 2, o: 2, t: 1, r: 4} to form a word, what is the expected number of matches of the pattern 'or*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 9, c: 6}. What is the expected number of occurrences of the pattern 'cf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {n: 2, j: 4, l: 3, c: 1, h: 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 6, u: 4, r: 5}. What is the expected number of occurrences of the pattern 'r+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": "0.35", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 6, j: 6, n: 2}, what is the expected number of times the pattern 'n.*a' 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": "When randomly selecting 5 letters from the multiset {i: 5, c: 7, x: 3} to form a word, what is the expected number of matches of the pattern 'i+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 2, s: 3, z: 4, p: 3}, what is the expected number of times the pattern 'ms+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 4, v: 2, k: 5, u: 2, m: 2} 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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 4, y: 1, e: 4, j: 1} 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": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {k: 7, d: 3, f: 5}. What is the expected number of occurrences of the pattern 'd.*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": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, i: 2, f: 5, l: 3}. What is the expected number of occurrences of the pattern 'f*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, x: 5, v: 2, g: 4}, what is the expected number of times the pattern 'vg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 7, r: 8}, what is the expected number of times the pattern 'n.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 6, b: 2, k: 6}. What is the expected number of occurrences of the pattern 'kf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 5, s: 5, i: 3} to form a word, what is the expected number of matches of the pattern 's*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, m: 1, i: 4, w: 2}, what is the expected number of times the pattern 'm*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.96", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, o: 5, f: 2, m: 2}, what is the expected number of times the pattern 'x*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.44", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 3, j: 3, y: 1, p: 3, c: 3}. What is the expected number of occurrences of the pattern 'g*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": "1.42", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 6, i: 4}, what is the expected number of times the pattern 'il*' 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 {c: 6, r: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'r*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.42", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {l: 3, h: 5, j: 5} 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": "0.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 5, q: 3, x: 2, a: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 6, l: 4, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.38", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, l: 3, b: 3, d: 2, w: 1}. What is the expected number of occurrences of the pattern 'w+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": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 10, z: 3}, what is the expected number of times the pattern 'z+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.88", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 5, q: 1, x: 2, o: 2, m: 3}, what is the expected number of times the pattern 'xq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.82", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 2, n: 5, c: 2, g: 2}. What is the expected number of occurrences of the pattern 'c+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": "0.16", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {q: 3, v: 3, z: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'mv+'? 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": "When randomly selecting 4 letters from the multiset {d: 1, o: 4, i: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'jd+'? 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 4 by randomly selecting letters from the multiset {w: 3, n: 1, k: 1, q: 1, i: 4}, what is the expected number of times the pattern 'n.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 3, d: 2, w: 2, f: 3, x: 1}, what is the expected number of times the pattern 'px*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 3, g: 2, b: 4, o: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, t: 7} to form a word, what is the expected number of matches of the pattern 't+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 3, o: 1, l: 1, n: 3, c: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 1, p: 3, w: 1, c: 2, b: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 5, c: 3, o: 3, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {b: 5, y: 4, l: 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": "0.77", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {t: 8, u: 7}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 6, f: 5} to form a word, what is the expected number of matches of the pattern 'fu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.02", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 3, d: 2, b: 2, z: 1, x: 2} 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": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, q: 3, j: 2, d: 2}, what is the expected number of times the pattern 'qw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, u: 7, g: 3}. What is the expected number of occurrences of the pattern 'lg+' in 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": "When randomly selecting 5 letters from the multiset {g: 3, l: 2, h: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'g*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.98", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 6, j: 9}. 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": "3.74", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 4, m: 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, s: 7}, what is the expected number of times the pattern 'q+s' 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 4 by randomly selecting letters from the multiset {r: 5, g: 1, n: 3, m: 4}, what is the expected number of times the pattern 'r*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, y: 2, a: 5}, what is the expected number of times the pattern 'd.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 4, d: 3, x: 2, f: 2, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {x: 4, i: 2, e: 2, q: 3, h: 2}. What is the expected number of occurrences of the pattern 'h*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": "0.88", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, l: 1, k: 2, b: 4}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 4, g: 10} to form a word, what is the expected number of matches of the pattern 'ig+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 5, u: 1, t: 2, z: 2}, 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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 5, u: 2, q: 4}. What is the expected number of occurrences of the pattern 'uu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 3, i: 3, w: 3, c: 4, u: 1}, what is the expected number of times the pattern 'iw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 7, l: 4, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 3, x: 4, v: 6, 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": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 6, i: 4}, 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 1, j: 1, c: 3, h: 3, n: 2}. What is the expected number of occurrences of the pattern 'c.*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 {j: 2, z: 4, l: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'jh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 3, d: 4, z: 4, y: 3} to form a word, what is the expected number of matches of the pattern 'yz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 4, j: 3, p: 2, w: 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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 2, b: 3, e: 3, t: 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": "0.82", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 2, g: 3, c: 6}, what is the expected number of times the pattern 'f.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, h: 3, g: 6}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, z: 3, c: 2, e: 3}, what is the expected number of times the pattern 'q+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.28", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 1, k: 3, m: 3, a: 4, t: 2}. What is the expected number of occurrences of the pattern 'km*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.42", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {z: 7, t: 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": "2.69", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 4, q: 3, h: 8}, 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": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 2, r: 5, l: 3, x: 3}. What is the expected number of occurrences of the pattern 'r.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.38", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 8, n: 5} to form a word, what is the expected number of matches of the pattern 'h+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.77", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 6, a: 3, c: 4, e: 1}, what is the expected number of times the pattern 'c+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {c: 6, t: 5} to form a word, what is the expected number of matches of the pattern 't*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.29", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 6, b: 6} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 8, p: 5}, what is the expected number of times the pattern 'pb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 9, o: 3}, what is the expected number of times the pattern 'o.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, o: 1, a: 1, p: 3, t: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 4, u: 9}. 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": "2.77", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {g: 5, z: 2, a: 3, q: 3, d: 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": "0.11", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 8, x: 3}, what is the expected number of times the pattern 'hx*' appears? 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 {l: 1, c: 5, f: 4, e: 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": "2.32", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, q: 4, i: 3, g: 3}. What is the expected number of occurrences of the pattern 'q*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, c: 2, o: 4, d: 4, x: 1}. 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 5, r: 5} to form a word, what is the expected number of matches of the pattern 'jr*'? 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 4 letters from the multiset {w: 5, y: 1, d: 2, c: 2, f: 3}. What is the expected number of occurrences of the pattern 'c+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": "0.04", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 4, i: 3, r: 7}, what is the expected number of times the pattern 'ti+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 5, e: 4, a: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 1, r: 2, u: 1, n: 3, k: 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, a: 1, q: 5, b: 1, h: 2}, what is the expected number of times the pattern 'hh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 4, c: 4, q: 2, x: 1}, what is the expected number of times the pattern 'k*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 6, q: 7}, what is the expected number of times the pattern 'n+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 7, n: 3, b: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 3, h: 1, a: 2, l: 4}. What is the expected number of occurrences of the pattern 'lh*' 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 4 by randomly selecting letters from the multiset {h: 2, s: 2, d: 3, v: 2, k: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, t: 3, f: 2, g: 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 {b: 1, o: 4, v: 1, x: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 2, t: 4, b: 1, m: 4, e: 4}, 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": "1.49", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {g: 4, w: 4, i: 3, q: 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": "0.38", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 5, u: 4, i: 6}, 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": "0.86", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 5, s: 8}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.59", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {u: 4, i: 3, y: 4}. What is the expected number of occurrences of the pattern 'iy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {j: 10, f: 5} 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": "0.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 3, x: 1, r: 3, v: 3, g: 3}. What is the expected number of occurrences of the pattern 'gr*' in 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": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 3, q: 7}, what is the expected number of times the pattern 'q+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 2, k: 3, s: 4, x: 3, p: 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, z: 7}, what is the expected number of times the pattern 'zn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.63", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 5, e: 10}. 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": "1.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 5, o: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'yo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.49", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, l: 1, v: 4, x: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 5, u: 5, j: 5}, what is the expected number of times the pattern 'uj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 4, s: 2, b: 4, a: 3, v: 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, h: 2, k: 3, n: 3, j: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 5, d: 9}, what is the expected number of times the pattern 'di*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {x: 1, y: 4, k: 5} 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": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, s: 4, a: 5}, what is the expected number of times the pattern 'vs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 4, r: 3, d: 1, t: 4, e: 2}, what is the expected number of times the pattern 'td+' 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 {f: 2, e: 3, l: 2, h: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 5, q: 10}, what is the expected number of times the pattern 'a.*q' 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 {w: 3, q: 3, u: 1, h: 3, c: 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": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 7, o: 3, s: 3}, 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": "1.51", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {v: 3, j: 4, y: 7}. What is the expected number of occurrences of the pattern 'vy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 1, m: 4, l: 1, y: 2, n: 3}, what is the expected number of times the pattern 'n*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 4, w: 3, u: 2, o: 2, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, s: 6}. What is the expected number of occurrences of the pattern 'h.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 2, m: 3, d: 4, r: 1}, what is the expected number of times the pattern 'r*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 5, m: 2, x: 1, b: 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, v: 1, h: 4, s: 3}, what is the expected number of times the pattern 'v*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 1, o: 3, s: 6, m: 2} to form a word, what is the expected number of matches of the pattern 'sm+'? 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 {x: 2, v: 4, d: 2, s: 1, q: 1} 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 8, t: 7}, what is the expected number of times the pattern 's+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, m: 4}, 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 1, i: 2, o: 3, l: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'wl+'? 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 {x: 3, p: 3, w: 4, z: 3}, 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": "0.26", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, u: 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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {s: 2, e: 4, v: 4, g: 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": "0.88", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {p: 3, j: 5, c: 7} to form a word, what is the expected number of matches of the pattern 'j.*p'? 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 4 by randomly selecting letters from the multiset {w: 2, z: 2, u: 4, y: 2}, what is the expected number of times the pattern 'w*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.94", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, t: 2, h: 3, u: 2, v: 2}. What is the expected number of occurrences of the pattern 't.*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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, f: 4, d: 2, l: 5}, what is the expected number of times the pattern 'ld*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, p: 1, s: 1, a: 3, g: 2}. 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": "Form a word by randomly choosing 5 letters from the multiset {v: 3, i: 6, w: 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": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {e: 3, w: 2, m: 3, y: 3} 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": "0.82", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 2, h: 2, d: 3, e: 3} 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 6, k: 4}. What is the expected number of occurrences of the pattern 'k.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {s: 3, n: 3, p: 3, v: 2}. What is the expected number of occurrences of the pattern 'n+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": "0.19", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, e: 3, o: 1, d: 5, i: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {i: 8, q: 4}. 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": "4.24", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 6, s: 6}, what is the expected number of times the pattern 'z.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 3, r: 2, x: 6} to form a word, what is the expected number of matches of the pattern 'x.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 2, z: 4, d: 2, n: 4}, 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": "0.55", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {n: 1, a: 2, m: 2, y: 2, w: 4}. What is the expected number of occurrences of the pattern 'nw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 2, y: 2, z: 4, l: 3} to form a word, what is the expected number of matches of the pattern 'oy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.12", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 3, x: 3, a: 4, l: 2, q: 3} to form a word, what is the expected number of matches of the pattern 'al*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.49", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 5, a: 5, x: 3}, what is the expected number of times the pattern 's*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 6, r: 6}, what is the expected number of times the pattern 'z.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 4, r: 4, f: 2}. What is the expected number of occurrences of the pattern 'd*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, a: 4, y: 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": "1.09", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 4, v: 5, c: 3}, what is the expected number of times the pattern 'av+' 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": "When randomly selecting 4 letters from the multiset {d: 4, g: 3, n: 1, p: 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": "0.28", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 2, l: 4, n: 5} to form a word, what is the expected number of matches of the pattern 'ln*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.19", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 4, u: 5, t: 4}, 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": "0.46", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {m: 5, x: 10}. 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": "4.29", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {a: 2, r: 4, q: 3, v: 1, b: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {o: 5, z: 2, n: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.22", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {r: 3, e: 3, p: 3, l: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, i: 3, v: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'f.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, h: 5, l: 4, j: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 1, b: 5, v: 2, z: 4}, 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": "0.89", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, o: 5, b: 3, u: 2, y: 3}, what is the expected number of times the pattern 'sy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, v: 3, c: 1, u: 4}, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 1, l: 1, z: 5, s: 2, b: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 6, b: 4}, 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, u: 4, e: 1, f: 1, x: 3}, what is the expected number of times the pattern 'ea+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}