messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"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"
}
] | 0.06 | MATH |
[
{
"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"
}
] | 1.17 | MATH |
[
{
"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"
}
] | 1.15 | MATH |
[
{
"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"
}
] | 0.33 | MATH |
[
{
"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"
}
] | 0.64 | MATH |
[
{
"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"
}
] | 0.2 | MATH |
[
{
"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"
}
] | 0.14 | MATH |
[
{
"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"
}
] | 1.29 | MATH |
[
{
"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"
}
] | 0.27 | MATH |
[
{
"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"
}
] | 0.1 | MATH |
[
{
"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"
}
] | 0.05 | MATH |
[
{
"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"
}
] | 0.33 | MATH |
[
{
"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"
}
] | 0.8 | MATH |
[
{
"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"
}
] | 0.61 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 0.32 | MATH |
[
{
"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"
}
] | 0.43 | MATH |
[
{
"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"
}
] | 0.08 | MATH |
[
{
"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"
}
] | 1.08 | MATH |
[
{
"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"
}
] | 0.48 | MATH |
[
{
"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"
}
] | 1.17 | MATH |
[
{
"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"
}
] | 0.46 | MATH |
[
{
"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"
}
] | 1.84 | MATH |
[
{
"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"
}
] | 1.53 | MATH |
[
{
"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"
}
] | 0.14 | MATH |
[
{
"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"
}
] | 0.11 | MATH |
[
{
"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"
}
] | 0.64 | MATH |
[
{
"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"
}
] | 0.08 | MATH |
[
{
"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"
}
] | 0.12 | MATH |
[
{
"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"
}
] | 0.4 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 1.36 | MATH |
[
{
"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"
}
] | 0.21 | MATH |
[
{
"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"
}
] | 0.32 | MATH |
[
{
"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"
}
] | 1.18 | MATH |
[
{
"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"
}
] | 0.1 | MATH |
[
{
"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"
}
] | 0.31 | MATH |
[
{
"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"
}
] | 0.24 | MATH |
[
{
"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"
}
] | 0.21 | MATH |
[
{
"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"
}
] | 0.2 | MATH |
[
{
"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"
}
] | 1.24 | MATH |
[
{
"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"
}
] | 0.46 | MATH |
[
{
"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"
}
] | 0.05 | MATH |
[
{
"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"
}
] | 0.19 | MATH |
[
{
"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"
}
] | 0.27 | MATH |
[
{
"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"
}
] | 1.14 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 2.0 | MATH |
[
{
"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"
}
] | 1.64 | MATH |
[
{
"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"
}
] | 0.4 | MATH |
[
{
"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"
}
] | 0.07 | MATH |
[
{
"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"
}
] | 1.14 | MATH |
[
{
"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"
}
] | 1.29 | MATH |
[
{
"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"
}
] | 0.17 | MATH |
[
{
"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"
}
] | 0.25 | MATH |
[
{
"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"
}
] | 2.21 | MATH |
[
{
"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"
}
] | 1.85 | MATH |
[
{
"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"
}
] | 0.27 | MATH |
[
{
"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"
}
] | 0.15 | MATH |
[
{
"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"
}
] | 0.67 | MATH |
[
{
"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"
}
] | 0.04 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 0.05 | MATH |
[
{
"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"
}
] | 2.66 | MATH |
[
{
"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"
}
] | 0.9 | MATH |
[
{
"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"
}
] | 0.33 | MATH |
[
{
"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"
}
] | 0.72 | MATH |
[
{
"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"
}
] | 0.72 | MATH |
[
{
"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"
}
] | 0.27 | MATH |
[
{
"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"
}
] | 0.19 | MATH |
[
{
"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"
}
] | 0.45 | MATH |
[
{
"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"
}
] | 0.8 | MATH |
[
{
"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"
}
] | 0.8 | MATH |
[
{
"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"
}
] | 0.08 | MATH |
[
{
"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"
}
] | 1.27 | MATH |
[
{
"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"
}
] | 1.0 | MATH |
[
{
"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"
}
] | 0.5 | MATH |
[
{
"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"
}
] | 0.21 | MATH |
[
{
"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"
}
] | 0.68 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 1.61 | MATH |
[
{
"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"
}
] | 0.13 | MATH |
[
{
"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"
}
] | 0.27 | MATH |
[
{
"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"
}
] | 0.67 | MATH |
[
{
"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"
}
] | 0.23 | MATH |
[
{
"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"
}
] | 0.0 | MATH |
[
{
"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"
}
] | 0.07 | MATH |
[
{
"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"
}
] | 2.98 | MATH |
[
{
"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"
}
] | 2.21 | MATH |
[
{
"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"
}
] | 0.1 | MATH |
[
{
"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"
}
] | 0.94 | MATH |
[
{
"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"
}
] | 2.43 | MATH |
[
{
"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"
}
] | 0.11 | MATH |
[
{
"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"
}
] | 1.11 | MATH |
[
{
"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"
}
] | 1.14 | MATH |
[
{
"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"
}
] | 0.7 | MATH |
[
{
"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"
}
] | 0.71 | MATH |
[
{
"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"
}
] | 0.36 | MATH |
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