messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 4, w: 3, u: 1}, what is the expected number of times the pattern 'o+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.03 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, r: 4, v: 2, c: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 2, g: 2, t: 3, z: 1, a: 4} to form a word, what is the expected number of matches of the pattern 'tz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 3, f: 2, o: 3, d: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 1, x: 1, o: 2, l: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, e: 2, z: 2, a: 3}. What is the expected number of occurrences of the pattern 'ze+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.24 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, v: 5}. What is the expected number of occurrences of the pattern 'uv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.05 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, o: 2, c: 3, y: 2, k: 3}, what is the expected number of times the pattern 'o+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, q: 2, u: 3, e: 1, i: 1}, what is the expected number of times the pattern 'iu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.38 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, j: 2, t: 2, d: 2, o: 2}, what is the expected number of times the pattern 't.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, z: 2, o: 4}, what is the expected number of times the pattern 'zv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.19 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, y: 4}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 3, n: 4, z: 2}. What is the expected number of occurrences of the pattern 'g+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, t: 1, p: 1, y: 3, c: 4}, what is the expected number of times the pattern 'c*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.07 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, w: 3, t: 3}, what is the expected number of times the pattern 't*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.29 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, n: 4, p: 3}. What is the expected number of occurrences of the pattern 'r*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 3, d: 1, l: 1, u: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'lu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.09 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 6, r: 1, v: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 5, m: 6}, what is the expected number of times the pattern 'x+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.11 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, t: 4, k: 2}, what is the expected number of times the pattern 'et*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.29 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 7, l: 5} to form a word, what is the expected number of matches of the pattern 'l.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.59 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {o: 3, e: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {h: 3, i: 8} to form a word, what is the expected number of matches of the pattern 'i+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.61 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {h: 1, o: 3, r: 1, c: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'r.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.14 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 3, h: 2, o: 5} to form a word, what is the expected number of matches of the pattern 'i.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 2, f: 1, j: 2, i: 5} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {z: 3, u: 3, a: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'u.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, e: 1, c: 3, x: 3, v: 1}. What is the expected number of occurrences of the pattern 'fc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.04 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {m: 5, u: 5}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, z: 7} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.25 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'js*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 2, h: 4, e: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'hw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.44 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 5, f: 6}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, c: 2, b: 3, q: 3}. What is the expected number of occurrences of the pattern 'gg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.93 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, l: 1, z: 2, v: 1, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 4, s: 6, z: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 1, t: 1, x: 2, q: 2, n: 2}, what is the expected number of times the pattern 'q.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.43 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, h: 2, j: 2, c: 3, y: 3}, what is the expected number of times the pattern 'jy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.19 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, d: 2, e: 2}. What is the expected number of occurrences of the pattern 'qe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.31 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, a: 2, k: 1, v: 4, j: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 6, r: 2} to form a word, what is the expected number of matches of the pattern 'rf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.14 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 9, z: 3}. What is the expected number of occurrences of the pattern 'z+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, z: 1, a: 2, h: 3, b: 2}. What is the expected number of occurrences of the pattern 'az+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, e: 5, a: 2, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 5, b: 2, w: 1, c: 1}, what is the expected number of times the pattern 'c.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 1, u: 1, s: 2, m: 2, v: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, f: 3, m: 3}, what is the expected number of times the pattern 'm.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 5, s: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.83 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 3, d: 1, u: 4} to form a word, what is the expected number of matches of the pattern 'uj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.8 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, z: 1, f: 3, d: 2, p: 1}. What is the expected number of occurrences of the pattern 'z.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, v: 4, e: 4, n: 2}, what is the expected number of times the pattern 't*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.53 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, q: 2, h: 1, g: 3}. What is the expected number of occurrences of the pattern 'qh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.06 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {y: 3, o: 5, k: 2} to form a word, what is the expected number of matches of the pattern 'o*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.32 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, m: 2, o: 6}, what is the expected number of times the pattern 'to+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.72 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 8, d: 4}, what is the expected number of times the pattern 'z.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 1, u: 3, z: 1, l: 4}, what is the expected number of times the pattern 'u*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.38 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 5, o: 5}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, z: 2, o: 2, w: 1, s: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 1, d: 4, s: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'sw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 4, j: 6} to form a word, what is the expected number of matches of the pattern 'jb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.63 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 5, o: 4} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 4, q: 4} to form a word, what is the expected number of matches of the pattern 'q.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.86 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, o: 3, b: 3, p: 1, u: 2}, what is the expected number of times the pattern 'up*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 1, p: 2, n: 4, o: 3, y: 1} to form a word, what is the expected number of matches of the pattern 'k.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 5, c: 1, g: 4}, what is the expected number of times the pattern 'g+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 6, l: 4}, what is the expected number of times the pattern 'kl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.43 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, n: 6, k: 2}, what is the expected number of times the pattern 'n*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, x: 3, i: 7}, what is the expected number of times the pattern 'gi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.78 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, j: 1, c: 4, w: 2, o: 2}. What is the expected number of occurrences of the pattern 'h+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.04 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 11, a: 1}. What is the expected number of occurrences of the pattern 'd*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.83 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, b: 1, a: 1, g: 4, p: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 4, p: 4} to form a word, what is the expected number of matches of the pattern 'p.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.86 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 7, n: 5}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 2, o: 1, x: 3, w: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.11 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, d: 2, q: 2, o: 3, p: 2}. What is the expected number of occurrences of the pattern 'o*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 5, r: 4}, what is the expected number of times the pattern 'kr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 1, z: 4, l: 1, u: 3, q: 3}, what is the expected number of times the pattern 'yq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.41 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 6, p: 5}. What is the expected number of occurrences of the pattern 'lp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.11 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, j: 5, f: 1, p: 2}, what is the expected number of times the pattern 'c+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.36 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 6, n: 4} to form a word, what is the expected number of matches of the pattern 'ni*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.83 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 4, m: 7} to form a word, what is the expected number of matches of the pattern 'gm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.68 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, j: 3, p: 5}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.91 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 2, y: 2, z: 1, a: 5} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, w: 3, h: 3, z: 1}, what is the expected number of times the pattern 'zw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, n: 4, m: 1, s: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, w: 2, g: 4, z: 2}. What is the expected number of occurrences of the pattern 'w+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.14 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, g: 5, n: 3}. What is the expected number of occurrences of the pattern 'n*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.29 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 2, v: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, o: 6}. What is the expected number of occurrences of the pattern 'o.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 4, h: 4, u: 4} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, y: 2, z: 2, a: 1, r: 1}. What is the expected number of occurrences of the pattern 'aa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 2, x: 1, g: 4, t: 4} to form a word, what is the expected number of matches of the pattern 'gx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.56 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 6, m: 3}. What is the expected number of occurrences of the pattern 'v+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.68 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 4, t: 3, l: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'r.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, j: 2, g: 4}. What is the expected number of occurrences of the pattern 'g*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.62 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, v: 2, d: 2, a: 1, g: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.21 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 3, u: 2, z: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'z.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {w: 4, g: 3, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, o: 1, p: 1, s: 2, n: 2}. What is the expected number of occurrences of the pattern 'sn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 3, i: 2, h: 3, x: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'h+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
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