messages listlengths 1 1 | ground_truth stringclasses 38 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "When randomly selecting 3 letters from the multiset {e: 2, a: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'a+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, l: 1, j: 1, b: 1, x: 2}. What is the expected number of occurrences of the pattern 'r+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, y: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, a: 2, o: 2}, 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"
}
] | 0.3 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, r: 1, b: 2}, what is the expected number of times the pattern 'r.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, x: 3, d: 2}, what is the expected number of times the pattern 'md+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 2, e: 1, l: 1, b: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, g: 1, o: 3, m: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, w: 1, y: 1, o: 1, t: 2}, what is the expected number of times the pattern 'o.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, j: 2, s: 1, n: 1, q: 1} 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, z: 1, f: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'f*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, m: 2, t: 1, b: 2}, what is the expected number of times the pattern 'm*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, l: 2}. What is the expected number of occurrences of the pattern 'l*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, l: 1, o: 2, c: 1}, 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"
}
] | 1.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, b: 1, q: 1, h: 2, c: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, r: 2, m: 1, f: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, t: 3}. What is the expected number of occurrences of the pattern 'f.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, v: 1, k: 2, t: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, u: 4}, 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"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {i: 2, j: 1, a: 1, r: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'i.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {x: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, k: 2, t: 2}. What is the expected number of occurrences of the pattern 'h*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 2, l: 2, p: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 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}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, m: 1, c: 1, r: 3}, what is the expected number of times the pattern 'x+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, l: 2, j: 1, f: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, g: 1, p: 1, q: 1}. What is the expected number of occurrences of the pattern 'u*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 1, b: 1, i: 2, p: 1, z: 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}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {h: 1, i: 1, o: 1, t: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'ih+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 5, h: 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"
}
] | 2.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, u: 4}. What is the expected number of occurrences of the pattern 'ur*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, d: 3}, what is the expected number of times the pattern 'd*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.25 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {z: 2, h: 4} 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"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, f: 1, w: 1, s: 1, a: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, v: 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"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, t: 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"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, s: 2, h: 1}. 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"
}
] | 0.75 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {i: 2, h: 2, r: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 4, q: 2} 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"
}
] | 0.73 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {e: 4, m: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'm.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, k: 2}. What is the expected number of occurrences of the pattern 'vk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, u: 1, l: 2, q: 1}. What is the expected number of occurrences of the pattern 'ul*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 5, e: 1}. What is the expected number of occurrences of the pattern 'et+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, n: 1, y: 2}, what is the expected number of times the pattern 'y*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.95 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, u: 1, q: 1, f: 2, h: 1}. What is the expected number of occurrences of the pattern 'fu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, k: 1, m: 1, c: 2}. What is the expected number of occurrences of the pattern 'mc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, l: 3, s: 1, t: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, w: 2, o: 1, u: 1, f: 1}, 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"
}
] | 0.57 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, t: 2, o: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, r: 1, h: 1, z: 2, e: 1}, 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, y: 2, k: 2}, what is the expected number of times the pattern 'k.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, q: 1, j: 2, b: 1, h: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, n: 1, x: 2, h: 1, i: 1}. 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"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, l: 1, w: 1, r: 2, x: 1}, 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"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, f: 1, a: 2}, 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}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, h: 1, t: 1, o: 2, r: 1}, what is the expected number of times the pattern 'r*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, k: 2, m: 2, j: 1}, what is the expected number of times the pattern 'a.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 2, m: 3}, what is the expected number of times the pattern 'lf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 4, k: 1}. What is the expected number of occurrences of the pattern 'w.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, h: 1, f: 2, n: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 1, p: 2, t: 1, x: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'mx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, y: 2, f: 2, c: 1}. What is the expected number of occurrences of the pattern 'y+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, d: 1, x: 2, j: 1, y: 1}, 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"
}
] | 1.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {x: 2, 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"
}
] | 1.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 4, o: 2} to form a word, what is the expected number of matches of the pattern 't+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, w: 1, u: 2, v: 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 2, l: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'rl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, e: 1, c: 4}. What is the expected number of occurrences of the pattern 'me+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, o: 1, p: 2, s: 1, l: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, b: 2, g: 2, p: 1}. What is the expected number of occurrences of the pattern 'zb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, l: 2, s: 1, e: 2}. What is the expected number of occurrences of the pattern 'k+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, a: 1, c: 1, j: 1, h: 2}, what is the expected number of times the pattern 'vj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, o: 1, r: 1, i: 1, w: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {z: 4, n: 1, 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"
}
] | 1.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {l: 2, e: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'n+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, d: 1, x: 1, n: 3}, what is the expected number of times the pattern 'n*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, i: 1, t: 2, m: 2}. What is the expected number of occurrences of the pattern 't.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, l: 1, u: 2, h: 2}. What is the expected number of occurrences of the pattern 'l*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, e: 1, q: 2, n: 1}, what is the expected number of times the pattern 'eq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, r: 2}, what is the expected number of times the pattern 'd*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, o: 3, q: 1, j: 1}. What is the expected number of occurrences of the pattern 'q.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 1, g: 3, a: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, o: 1, b: 1, h: 1}, what is the expected number of times the pattern 'h+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, c: 3, r: 1}. What is the expected number of occurrences of the pattern 'cw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 1, c: 1, v: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'u.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, g: 1, m: 1, h: 1, r: 1}, what is the expected number of times the pattern 'hr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, z: 1, b: 1, o: 2, t: 1}, what is the expected number of times the pattern 'or*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 1, k: 1, f: 1, w: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'pl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, u: 1, r: 1, z: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'p+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, d: 4}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, b: 1, v: 1, o: 1, p: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, g: 1, q: 2, i: 2}. What is the expected number of occurrences of the pattern 'qg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {v: 2, i: 1, c: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'v+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 3, h: 2, m: 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}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, p: 2, b: 1, w: 1, s: 1}. What is the expected number of occurrences of the pattern 'ws*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, i: 1, p: 2, c: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
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