messages listlengths 1 1 | ground_truth stringclasses 65 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, x: 4, p: 3, k: 1}, what is the expected number of times the pattern 'pk+' 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 4 by randomly selecting letters from the multiset {y: 4, s: 2, q: 3}, what is the expected number of times the pattern 'qs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.61 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 3, o: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'o+k'? 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 {o: 2, j: 2, g: 2, y: 1, i: 2} 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"
}
] | 0.54 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, m: 7}. What is the expected number of occurrences of the pattern 'm*c' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 4, n: 1, a: 4}, what is the expected number of times the pattern 'na+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 2, v: 1, s: 3, r: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'vw+'? Round 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 {r: 2, q: 5, o: 2}. What is the expected number of occurrences of the pattern 'o*r' in each word? Round your answer 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 4 by randomly selecting letters from the multiset {e: 3, m: 6}, what is the expected number of times the pattern 'em+' appears? 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 {f: 1, v: 4, b: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, c: 2, x: 1, b: 3, 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, s: 1, r: 3, m: 1, i: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 3, m: 1, q: 2, r: 2, x: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 5, s: 4} to form a word, what is the expected number of matches of the pattern 'z+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.23 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, r: 4, q: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, k: 2, b: 1, g: 2, e: 1}. What is the expected number of occurrences of the pattern 'k+u' 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 {d: 3, e: 3, w: 1, h: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'dh+'? 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 {g: 2, s: 2, x: 5}. 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"
}
] | 0.18 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 3, k: 1, u: 2, j: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'k.*d'? Round 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 4 letters from the multiset {b: 3, m: 5, e: 1}. What is the expected number of occurrences of the pattern 'em*' 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 4 letters from the multiset {i: 5, g: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? 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 {m: 1, o: 4, w: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'm.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {o: 5, y: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'yo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.62 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, g: 2, j: 3, q: 3}. What is the expected number of occurrences of the pattern 'v+g' 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": "When randomly selecting 4 letters from the multiset {s: 3, a: 1, j: 1, q: 1, x: 3} 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, s: 4, j: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 5, y: 4} to form a word, what is the expected number of matches of the pattern 'yc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.01 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 2, p: 4, t: 3} to form a word, what is the expected number of matches of the pattern 'tp*'? Round 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 {e: 5, r: 4} to form a word, what is the expected number of matches of the pattern 'e+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.23 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 3, g: 2, i: 4}, what is the expected number of times the pattern 'im+' 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 4 by randomly selecting letters from the multiset {t: 1, o: 2, p: 1, n: 3, g: 2}, what is the expected number of times the pattern 'ot*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.97 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, h: 4, b: 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"
}
] | 1.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, l: 2, t: 2, m: 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"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, d: 3, f: 2, u: 2}. What is the expected number of occurrences of the pattern 'u.*d' 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": "Form a word by randomly choosing 4 letters from the multiset {l: 3, g: 3, j: 3}. What is the expected number of occurrences of the pattern 'l.*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": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, p: 1, k: 1, s: 3, b: 1}, what is the expected number of times the pattern 'k*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.46 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 3, s: 2, u: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'u*s'? 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 4 by randomly selecting letters from the multiset {s: 6, v: 3}, what is the expected number of times the pattern 'v*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.57 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {w: 6, h: 3} to form a word, what is the expected number of matches of the pattern 'wh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 3, r: 1, f: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 2, i: 1, s: 1, o: 2, d: 3}. What is the expected number of occurrences of the pattern 'i.*d' 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 4 letters from the multiset {r: 2, v: 3, j: 4}. What is the expected number of occurrences of the pattern 'rv+' 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 4 letters from the multiset {n: 5, h: 4} to form a word, what is the expected number of matches of the pattern 'n+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.23 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 2, y: 5, e: 2}. What is the expected number of occurrences of the pattern 'v.*e' 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 4 letters from the multiset {e: 5, k: 4} to form a word, what is the expected number of matches of the pattern 'ke*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.01 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 4, r: 1, x: 1, c: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'w+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 3, c: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'zc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 1, d: 2, w: 2, z: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'ld*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.07 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, c: 3, x: 2, s: 1}. What is the expected number of occurrences of the pattern 'c+s' 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": "Form a word by randomly choosing 4 letters from the multiset {w: 3, b: 2, v: 4}. What is the expected number of occurrences of the pattern 'w.*b' 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": "Form a word by randomly choosing 4 letters from the multiset {g: 2, s: 5, f: 1, l: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, n: 3, w: 2, b: 2}, what is the expected number of times the pattern 'wn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.19 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 1, s: 2, u: 1, k: 2, r: 3}, what is the expected number of times the pattern 'u+s' appears? 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 4 letters from the multiset {d: 1, r: 4, i: 1, o: 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"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {y: 3, x: 3, l: 3}. What is the expected number of occurrences of the pattern 'ly+' 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 4 letters from the multiset {h: 2, j: 1, a: 1, y: 2, i: 3} 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"
}
] | 0.5 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {o: 2, h: 2, s: 1, j: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'j*x'? 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 {c: 1, b: 1, s: 1, h: 2, o: 4}. What is the expected number of occurrences of the pattern 'cb*' 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": "When randomly selecting 4 letters from the multiset {j: 2, k: 2, i: 2, s: 1, 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": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, v: 1, a: 2, w: 1, h: 2}, what is the expected number of times the pattern 'wt+' appears? 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 4 by randomly selecting letters from the multiset {o: 4, b: 5}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, f: 7}, what is the expected number of times the pattern 'fs+' 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 4 letters from the multiset {a: 1, n: 5, b: 3} 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 4 by randomly selecting letters from the multiset {a: 5, x: 4}, what is the expected number of times the pattern 'x+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.11 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 1, h: 4, n: 4} to form a word, what is the expected number of matches of the pattern 'nh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.67 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, q: 4, u: 2, l: 2}. What is the expected number of occurrences of the pattern 'ux*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.97 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 3, b: 1, h: 4, n: 1}. 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"
}
] | 0.5 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 2, n: 1, w: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'w+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.44 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, x: 6}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.5 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 2, h: 1, t: 4, b: 2} 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"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, p: 4, x: 2, q: 1}. What is the expected number of occurrences of the pattern 'dq+' 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 4 by randomly selecting letters from the multiset {o: 2, y: 1, e: 3, f: 3}, 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, o: 3, f: 4}, 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"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, x: 2, o: 3, e: 2}. What is the expected number of occurrences of the pattern 'f*o' 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": "When randomly selecting 4 letters from the multiset {o: 1, g: 4, a: 1, e: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'ge+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, v: 2, d: 2, l: 2, q: 2}, what is the expected number of times the pattern 'cq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.54 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 1, u: 5, i: 3}, what is the expected number of times the pattern 'u.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.42 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 1, p: 4, s: 1, u: 3}, what is the expected number of times the pattern 'su*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, b: 1, r: 1, t: 4}. 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"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, b: 2, g: 1, u: 1, h: 4}. 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"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, q: 2, v: 1, u: 4}. 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"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, v: 7}. What is the expected number of occurrences of the pattern 'v.*f' in each word? Round your answer 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 {o: 2, m: 1, t: 1, x: 3, z: 2}, what is the expected number of times the pattern 'ot+' appears? 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 4 letters from the multiset {v: 3, w: 2, l: 1, x: 1, o: 2}. What is the expected number of occurrences of the pattern 'vl+' 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 4 by randomly selecting letters from the multiset {n: 5, f: 4}, what is the expected number of times the pattern 'fn+' appears? 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, v: 3, a: 4} to form a word, what is the expected number of matches of the pattern 'va+'? 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 {n: 3, c: 6}, 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"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 1, x: 2, o: 2, c: 2, q: 2}, what is the expected number of times the pattern 'o+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.09 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 1, r: 2, k: 4, y: 1, q: 1}, what is the expected number of times the pattern 'k*x' 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 {m: 3, l: 6}, what is the expected number of times the pattern 'l.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, d: 6}, 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"
}
] | 1.5 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, m: 3, s: 1, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, b: 2, p: 1, z: 1, l: 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"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, d: 4}. 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"
}
] | 1.67 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 2, u: 3, l: 1, k: 3} 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"
}
] | 1.61 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 6, t: 3}. What is the expected number of occurrences of the pattern 't+l' 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 4 by randomly selecting letters from the multiset {v: 1, o: 2, y: 2, z: 2, u: 2}, what is the expected number of times the pattern 'y*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.07 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 5, w: 4}. What is the expected number of occurrences of the pattern 'wr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.01 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, p: 3, b: 1, w: 1, d: 3}, 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, n: 3, o: 4}. What is the expected number of occurrences of the pattern 'n+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 |
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