id stringlengths 39 39 | setting_key stringclasses 1
value | setting_name stringclasses 0
values | messages listlengths 1 1 | ground_truth stringclasses 126
values | dataset stringclasses 1
value |
|---|---|---|---|---|---|
combinatory_pattern_matching_train_0600 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {x: 5, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.29 | math |
combinatory_pattern_matching_train_0601 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, u: 1, i: 1, n: 2, h: 1}, what is the expected number of times the pattern 'hn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.23 | math |
combinatory_pattern_matching_train_0602 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, m: 3, p: 3}, what is the expected number of times the pattern 'l*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.36 | math |
combinatory_pattern_matching_train_0603 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, 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}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0604 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {v: 2, r: 1, a: 1, m: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0605 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {q: 1, o: 2, x: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'ro*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.86 | math |
combinatory_pattern_matching_train_0606 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, z: 3, d: 3}, what is the expected number of times the pattern 'd+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0607 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {m: 1, s: 3, z: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0608 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, h: 3, f: 2}, 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}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0609 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {z: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'zu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0610 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'y+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.75 | math |
combinatory_pattern_matching_train_0611 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {h: 4, y: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'y+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.24 | math |
combinatory_pattern_matching_train_0612 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, t: 1, a: 2}, what is the expected number of times the pattern 'ay*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.0 | math |
combinatory_pattern_matching_train_0613 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, q: 1, b: 1, i: 1, g: 2}, what is the expected number of times the pattern 'ib*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.77 | math |
combinatory_pattern_matching_train_0614 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, u: 4, l: 2}, what is the expected number of times the pattern 'u*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.6 | math |
combinatory_pattern_matching_train_0615 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, u: 1, d: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0616 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 2, h: 2, n: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0617 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, y: 2, g: 2, s: 1, l: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0618 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {x: 1, k: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0619 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, b: 3}. What is the expected number of occurrences of the pattern 'm+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.74 | math |
combinatory_pattern_matching_train_0620 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, m: 2, q: 2}. What is the expected number of occurrences of the pattern 'm*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0621 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, y: 4}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.2 | math |
combinatory_pattern_matching_train_0622 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {c: 1, q: 3, p: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'q*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0623 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 6, j: 2}, what is the expected number of times the pattern 'jg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.14 | math |
combinatory_pattern_matching_train_0624 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, l: 6}, what is the expected number of times the pattern 'l+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.14 | math |
combinatory_pattern_matching_train_0625 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 3, w: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'w*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.95 | math |
combinatory_pattern_matching_train_0626 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, d: 3, c: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0627 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {n: 2, s: 1, d: 4} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0628 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, z: 2, v: 1, q: 1}. What is the expected number of occurrences of the pattern 'z+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.15 | math |
combinatory_pattern_matching_train_0629 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, a: 1, y: 2, o: 3, v: 1}, what is the expected number of times the pattern 'o*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | math |
combinatory_pattern_matching_train_0630 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, x: 1, j: 2, w: 1, n: 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}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0631 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {j: 1, k: 1, h: 1, f: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'h+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0632 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {k: 1, a: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'k*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0633 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, b: 2, h: 1, k: 2}, what is the expected number of times the pattern 'k.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0634 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {b: 2, f: 2, x: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ff*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0635 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, r: 4}. 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}"
}
] | 1.33 | math |
combinatory_pattern_matching_train_0636 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {k: 1, u: 3, l: 4} to form a word, what is the expected number of matches of the pattern 'u.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0637 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, v: 1, a: 2, f: 1}, what is the expected number of times the pattern 'af+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.13 | math |
combinatory_pattern_matching_train_0638 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, a: 4, q: 1}. What is the expected number of occurrences of the pattern 'qa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0639 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, l: 4, g: 1, w: 2}. What is the expected number of occurrences of the pattern 'g.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0640 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 1, a: 2, g: 1, e: 1, v: 1}, what is the expected number of times the pattern 'we+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0641 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {h: 2, s: 1, d: 1, m: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0642 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, e: 3}, what is the expected number of times the pattern 'qe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0643 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, k: 2, h: 3}, what is the expected number of times the pattern 'h+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0644 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, z: 2, j: 2}, what is the expected number of times the pattern 'e+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.47 | math |
combinatory_pattern_matching_train_0645 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, e: 2, h: 1}, what is the expected number of times the pattern 'e+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.16 | math |
combinatory_pattern_matching_train_0646 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {o: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'do+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.25 | math |
combinatory_pattern_matching_train_0647 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, m: 3, o: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.64 | math |
combinatory_pattern_matching_train_0648 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {p: 2, j: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'pp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0649 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, o: 4}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.71 | math |
combinatory_pattern_matching_train_0650 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 1, w: 1, t: 1, v: 1, x: 2}. What is the expected number of occurrences of the pattern 'v.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0651 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, s: 2, e: 2, m: 1, g: 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}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0652 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {v: 3, w: 2, n: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'v*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.0 | math |
combinatory_pattern_matching_train_0653 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {h: 1, f: 1, n: 1, u: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0654 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 1, o: 3}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0655 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, h: 3, b: 2}. What is the expected number of occurrences of the pattern 'vv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | math |
combinatory_pattern_matching_train_0656 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, c: 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}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0657 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {j: 2, e: 1, z: 1, u: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'je+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0658 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {i: 1, x: 5} 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}"
}
] | 0.33 | math |
combinatory_pattern_matching_train_0659 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {l: 3, t: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0660 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, c: 1, m: 2, f: 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}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0661 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, q: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.29 | math |
combinatory_pattern_matching_train_0662 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {j: 1, e: 3, k: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'e*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.85 | math |
combinatory_pattern_matching_train_0663 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, m: 2, c: 3, l: 1}, what is the expected number of times the pattern 'e+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.08 | math |
combinatory_pattern_matching_train_0664 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, h: 1, x: 1, f: 3}, 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}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0665 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 4, w: 2, p: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0666 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, r: 2, k: 1, a: 1, q: 2}. What is the expected number of occurrences of the pattern 'cq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0667 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, s: 1, t: 1, m: 2}, what is the expected number of times the pattern 'st+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0668 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, d: 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}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0669 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {k: 1, m: 3, y: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0670 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, b: 4}, what is the expected number of times the pattern 'c+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.69 | math |
combinatory_pattern_matching_train_0671 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, j: 2, m: 1, h: 2}, what is the expected number of times the pattern 'he+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.25 | math |
combinatory_pattern_matching_train_0672 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, h: 3}. What is the expected number of occurrences of the pattern 'h+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.45 | math |
combinatory_pattern_matching_train_0673 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {y: 4, q: 4}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0674 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {v: 1, g: 2, q: 1, z: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'g*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.73 | math |
combinatory_pattern_matching_train_0675 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {b: 2, q: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'q+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0676 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, w: 4}. What is the expected number of occurrences of the pattern 'wu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.6 | math |
combinatory_pattern_matching_train_0677 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 1, n: 1, i: 1, e: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'id+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.15 | math |
combinatory_pattern_matching_train_0678 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, c: 2, g: 2}, what is the expected number of times the pattern 'g*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.2 | math |
combinatory_pattern_matching_train_0679 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, s: 2, u: 2, e: 1}, what is the expected number of times the pattern 'su*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.47 | math |
combinatory_pattern_matching_train_0680 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, t: 3, e: 1, p: 1, w: 1}, what is the expected number of times the pattern 'w.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0681 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 1, k: 1, e: 2, f: 1}, what is the expected number of times the pattern 'fe+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.15 | math |
combinatory_pattern_matching_train_0682 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {a: 2, t: 2, g: 1, k: 1, b: 1} 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0683 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, b: 3, r: 1, t: 1}, what is the expected number of times the pattern 'r+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0684 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, c: 2, d: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0685 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 2, z: 6}. What is the expected number of occurrences of the pattern 'za*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3.71 | math |
combinatory_pattern_matching_train_0686 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, c: 1, k: 3}, what is the expected number of times the pattern 'kd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0687 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, m: 1, r: 4, w: 1, q: 1}, what is the expected number of times the pattern 'i*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.41 | math |
combinatory_pattern_matching_train_0688 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, f: 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}"
}
] | 0.64 | math |
combinatory_pattern_matching_train_0689 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 6, s: 2}. What is the expected number of occurrences of the pattern 'fs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.46 | math |
combinatory_pattern_matching_train_0690 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, p: 1, h: 3, x: 1}, what is the expected number of times the pattern 'v*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.53 | math |
combinatory_pattern_matching_train_0691 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 1, z: 5}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0692 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, x: 3, s: 3}. What is the expected number of occurrences of the pattern 'x*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.0 | math |
combinatory_pattern_matching_train_0693 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 4, f: 2}, 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}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0694 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, z: 6}. What is the expected number of occurrences of the pattern 'z*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.14 | math |
combinatory_pattern_matching_train_0695 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 1, k: 1, j: 1, a: 2, r: 1}, what is the expected number of times the pattern 'k+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0696 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, m: 2, r: 1, n: 1, x: 1}, what is the expected number of times the pattern 'r*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.95 | math |
combinatory_pattern_matching_train_0697 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {z: 1, k: 1, y: 2, b: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.95 | math |
combinatory_pattern_matching_train_0698 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {b: 3, s: 1, e: 1, y: 1, j: 2} 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}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0699 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, l: 1, d: 2, y: 1, w: 1}, what is the expected number of times the pattern 'lw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.77 | math |
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