messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 3, w: 1, c: 1, l: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'uf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, y: 3, g: 2, a: 3}. What is the expected number of occurrences of the pattern 'e*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.46 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 1, m: 1, y: 2, j: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'ym+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.06 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, f: 1, q: 1, i: 2, x: 2}, what is the expected number of times the pattern 'f*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.97 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 1, l: 3, a: 1, g: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'l+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, f: 2, n: 4, o: 4}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, p: 1, r: 3, v: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.32 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 6, v: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.21 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 2, q: 7, k: 3} to form a word, what is the expected number of matches of the pattern 'kq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.72 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {w: 2, d: 2, q: 2, f: 6} to form a word, what is the expected number of matches of the pattern 'f+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, v: 4, s: 1, e: 2, k: 1}, what is the expected number of times the pattern 'ue*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.27 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, v: 1, u: 5, c: 1}. What is the expected number of occurrences of the pattern 'c*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.49 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 5, r: 3}, what is the expected number of times the pattern 'p*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.77 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 3, j: 2, r: 7} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, b: 1, f: 2, n: 2, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 4, u: 5} to form a word, what is the expected number of matches of the pattern 'du*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.01 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 7, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, d: 2, m: 2, o: 6}. What is the expected number of occurrences of the pattern 'o+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 2, h: 3, m: 3, w: 4} to form a word, what is the expected number of matches of the pattern 'm.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 3, k: 3, j: 1, r: 2, q: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.14 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {m: 5, q: 1, u: 3, s: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 6, i: 2, s: 1, k: 1}. What is the expected number of occurrences of the pattern 'ki+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, r: 5}, what is the expected number of times the pattern 'ra+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 1, e: 1, z: 3, k: 4} to form a word, what is the expected number of matches of the pattern 'ze+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, b: 2, t: 2, q: 2, v: 3}. What is the expected number of occurrences of the pattern 'tt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 2, y: 4, g: 2, p: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'yp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 5, p: 3, v: 4}, what is the expected number of times the pattern 't*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.02 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 7, f: 3}, what is the expected number of times the pattern 'fz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.37 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {e: 4, l: 5, v: 3} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.36 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 1, y: 3, d: 1, i: 3, v: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, j: 3, a: 3, n: 1, o: 1}, what is the expected number of times the pattern 'a+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, p: 3, r: 1, x: 1, f: 1}, what is the expected number of times the pattern 'fh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.62 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, o: 1, h: 1, e: 2, i: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, q: 1, d: 3, x: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 4, d: 1, g: 3, r: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'rg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, j: 3, a: 3, x: 2}, what is the expected number of times the pattern 'd*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, u: 4}. What is the expected number of occurrences of the pattern 'zu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {y: 1, c: 2, b: 2, a: 4, i: 2}. What is the expected number of occurrences of the pattern 'cy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 7, y: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, i: 4, r: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, g: 1, z: 3, j: 1, q: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 8, e: 4} to form a word, what is the expected number of matches of the pattern 'e.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.45 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 5, b: 2, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, q: 2, g: 2, m: 1}, what is the expected number of times the pattern 'a+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {y: 4, f: 2, q: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 5, u: 7} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, r: 2, o: 3}, what is the expected number of times the pattern 'oz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 7, s: 4}. What is the expected number of occurrences of the pattern 's.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.53 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, x: 3, s: 2, z: 1, e: 2}. What is the expected number of occurrences of the pattern 'je*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.69 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 5, f: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'f.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.49 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, j: 2, i: 2, r: 1, k: 1}, what is the expected number of times the pattern 'i.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, t: 1, q: 2, z: 3, x: 3}, what is the expected number of times the pattern 'ct*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.78 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 3, l: 4}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, r: 4, i: 3, o: 1}, what is the expected number of times the pattern 'oi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.12 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 6, n: 2}. What is the expected number of occurrences of the pattern 'y+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.61 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, s: 2, c: 3, m: 2}, what is the expected number of times the pattern 'c*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.92 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 5, w: 4}. What is the expected number of occurrences of the pattern 'v*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.05 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, o: 3, l: 1, e: 5}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 2, j: 3, z: 2, p: 5} to form a word, what is the expected number of matches of the pattern 'z.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 5, e: 3, w: 1}. What is the expected number of occurrences of the pattern 'q*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.26 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 5, k: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'xk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 4, s: 4} to form a word, what is the expected number of matches of the pattern 'a+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.71 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, q: 7}. What is the expected number of occurrences of the pattern 'q*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.94 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 3, u: 3, z: 4} to form a word, what is the expected number of matches of the pattern 'uz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.71 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 3, q: 4, s: 5} to form a word, what is the expected number of matches of the pattern 'sq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, k: 2, x: 4, i: 2}, what is the expected number of times the pattern 'ik*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.62 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 7, t: 4} to form a word, what is the expected number of matches of the pattern 't.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.76 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, q: 6, d: 4}. What is the expected number of occurrences of the pattern 'q*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 5, b: 4}. What is the expected number of occurrences of the pattern 'c*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.34 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 5, m: 4}, what is the expected number of times the pattern 'qm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.34 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {q: 5, u: 5} to form a word, what is the expected number of matches of the pattern 'u+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.69 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 4, m: 4, o: 2}, what is the expected number of times the pattern 'z*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.14 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, j: 2, w: 1, e: 2, r: 2}. What is the expected number of occurrences of the pattern 'wj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, c: 5, t: 2, x: 4}, what is the expected number of times the pattern 'c.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, b: 2, g: 4, o: 3}, what is the expected number of times the pattern 'ag+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 6, n: 6}, what is the expected number of times the pattern 'g.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 3, y: 2, e: 2, j: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'j.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 1, n: 3, b: 1, u: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'tt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 6, q: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 3, x: 3, i: 1, y: 3, v: 2}. What is the expected number of occurrences of the pattern 'y*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.41 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, r: 3, p: 1, e: 2, h: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {l: 5, v: 1, g: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'g.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, h: 1, a: 4, q: 1, j: 2}. What is the expected number of occurrences of the pattern 'hn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, s: 4, d: 3}, what is the expected number of times the pattern 'd*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.07 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 6, w: 1, m: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, b: 1, w: 2, s: 2}, what is the expected number of times the pattern 'ws*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.79 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {y: 1, r: 1, i: 2, h: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'yi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.39 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 5, w: 2, i: 2, v: 1, p: 1}, what is the expected number of times the pattern 'vu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 3, x: 2, e: 2, a: 1, f: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, k: 1, n: 6}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 4, y: 7}, what is the expected number of times the pattern 'w+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, c: 7, g: 4}, what is the expected number of times the pattern 's+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.06 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 4, m: 1, y: 3, t: 1}, what is the expected number of times the pattern 'y.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 6, t: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.25 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, r: 4, j: 5}, what is the expected number of times the pattern 'rq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.29 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {w: 3, h: 5, n: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 3, t: 1, q: 2, g: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'gq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, w: 3, y: 3}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.21 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 3, x: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'x.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, y: 1, h: 3, v: 4}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 7