messages
listlengths 1
1
| ground_truth
stringclasses 85
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, m: 1, s: 2, v: 2, h: 2}, 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 3, c: 3, i: 4} to form a word, what is the expected number of matches of the pattern 'jc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 2, q: 2, f: 3, e: 2, v: 1}, what is the expected number of times the pattern 'v+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 5 by randomly selecting letters from the multiset {m: 7, x: 3}, what is the expected number of times the pattern 'xm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.29
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 1, j: 3, s: 2, m: 1, g: 3}, what is the expected number of times the pattern 'wj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, b: 3, g: 4}, what is the expected number of times the pattern 'g.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 4, f: 6} to form a word, what is the expected number of matches of the pattern 'f.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {c: 3, n: 4, f: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round 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 5 letters from the multiset {l: 5, x: 5}. 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"
}
] |
2.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, a: 6, v: 1}, what is the expected number of times the pattern 'xv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.63
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {b: 3, d: 1, i: 1, g: 5} to form a word, what is the expected number of matches of the pattern 'dd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 4, j: 1, w: 1, s: 1, i: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 2, g: 2, x: 2, v: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'o*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 4, y: 2, x: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'dx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.66
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 5, a: 3, v: 2}. What is the expected number of occurrences of the pattern 'a.*a' 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 5 letters from the multiset {y: 1, d: 4, k: 3, r: 2}. What is the expected number of occurrences of the pattern 'r+y' 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": "When randomly selecting 5 letters from the multiset {b: 3, h: 2, n: 2, a: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'na*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 3, p: 4, g: 3}. What is the expected number of occurrences of the pattern 'h.*g' 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 5 letters from the multiset {q: 3, c: 3, d: 2, e: 2}. What is the expected number of occurrences of the pattern 'd*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 4, s: 4, h: 2}, what is the expected number of times the pattern 'hp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 1, f: 4, w: 3, r: 2}. 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"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {t: 4, a: 3, v: 2, f: 1} 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"
}
] |
0.1
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 2, k: 1, q: 1, a: 5, l: 1} to form a word, what is the expected number of matches of the pattern 'q*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {t: 4, g: 4, b: 2} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 2, p: 1, i: 2, m: 2, u: 3}, what is the expected number of times the pattern 'pi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 3, f: 6, q: 1} to form a word, what is the expected number of matches of the pattern 'l.*f'? 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 5 by randomly selecting letters from the multiset {j: 5, p: 5}, 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"
}
] |
2.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 1, f: 4, t: 5} to form a word, what is the expected number of matches of the pattern 'ht+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 3, o: 4, s: 3}, what is the expected number of times the pattern 'f*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 2, z: 3, d: 2, p: 3}, what is the expected number of times the pattern 'z.*z' appears? Round 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 5 letters from the multiset {o: 4, h: 6}. 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"
}
] |
3.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 5, g: 5}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 7, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' 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 5 letters from the multiset {j: 3, k: 3, r: 4}. What is the expected number of occurrences of the pattern 'kj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 5, w: 3, i: 2} 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"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, f: 2, k: 2, q: 2, j: 2}, what is the expected number of times the pattern 'j+f' 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 5 letters from the multiset {p: 6, w: 4}. What is the expected number of occurrences of the pattern 'w.*p' in each word? Round your answer 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 5 letters from the multiset {j: 4, e: 1, s: 2, n: 3}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, r: 1, u: 3, d: 2, n: 1}, what is the expected number of times the pattern 'r.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 5, l: 2, x: 3}, 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"
}
] |
2.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 6, z: 4}, what is the expected number of times the pattern 'qz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 2, p: 1, g: 3, l: 1, h: 3}, what is the expected number of times the pattern 'h+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 1, u: 1, g: 5, f: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'uo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 4, k: 6} to form a word, what is the expected number of matches of the pattern 'l*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 2, q: 3, j: 4, h: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 2, v: 2, f: 2, r: 1, a: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 6, q: 4} 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"
}
] |
1.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, z: 4, u: 4}, what is the expected number of times the pattern 'p+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 3, u: 7} 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"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 2, n: 8} 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"
}
] |
6.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 3, q: 7}, what is the expected number of times the pattern 'qe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.62
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 7, o: 3}. What is the expected number of occurrences of the pattern 'og*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.29
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 3, f: 2, i: 5}, what is the expected number of times the pattern 'f*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 2, x: 3, m: 5} to form a word, what is the expected number of matches of the pattern 'x*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 3, u: 7}. What is the expected number of occurrences of the pattern 'ou*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.29
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 4, r: 6}. What is the expected number of occurrences of the pattern 'rh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 3, x: 3, u: 4} to form a word, what is the expected number of matches of the pattern 'u*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.21
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 1, b: 3, y: 1, t: 5} to form a word, what is the expected number of matches of the pattern 't.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.56
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 5, a: 5} to form a word, what is the expected number of matches of the pattern 'y+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 2, e: 2, r: 3, s: 2, j: 1}, 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"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 2, v: 4, z: 4}, what is the expected number of times the pattern 'kz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 3, o: 1, l: 6} to form a word, what is the expected number of matches of the pattern 'mo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.63
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 4, 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"
}
] |
3.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, k: 3, n: 3, h: 2}. What is the expected number of occurrences of the pattern 'k.*k' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, u: 2, r: 3}, what is the expected number of times the pattern 'u+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.49
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 1, w: 4, n: 2, h: 3} 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 3, b: 7} to form a word, what is the expected number of matches of the pattern 'll*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 1, u: 6, g: 3} 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"
}
] |
3.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 2, l: 1, q: 3, z: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'zl+'? 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 5 by randomly selecting letters from the multiset {b: 2, u: 3, m: 2, n: 1, o: 2}, what is the expected number of times the pattern 'on+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.09
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 3, s: 1, g: 2, a: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 3, i: 1, v: 2, n: 1, b: 3}, what is the expected number of times the pattern 'n+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.13
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 1, f: 3, p: 2, o: 2, r: 2}. What is the expected number of occurrences of the pattern 'r+o' 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": "Form a word by randomly choosing 5 letters from the multiset {k: 6, r: 2, t: 2}. What is the expected number of occurrences of the pattern 'rt*' in each word? Round your answer 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 5 by randomly selecting letters from the multiset {r: 4, w: 2, e: 4}, 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"
}
] |
1.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, a: 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"
}
] |
1.8
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, j: 6}. 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 2, l: 7, k: 1}. What is the expected number of occurrences of the pattern 'k*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {z: 3, c: 2, w: 2, x: 1, f: 2}. What is the expected number of occurrences of the pattern 'c+w' 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": "Form a word by randomly choosing 5 letters from the multiset {w: 2, g: 4, t: 1, o: 2, b: 1}. What is the expected number of occurrences of the pattern 'o+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, f: 6, d: 2}. What is the expected number of occurrences of the pattern 'y*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.58
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 2, u: 4, z: 3, x: 1}. What is the expected number of occurrences of the pattern 'uo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 1, r: 4, u: 3, w: 2}. What is the expected number of occurrences of the pattern 'g.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 4, l: 2, b: 3, y: 1}, what is the expected number of times the pattern 'g+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.71
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 6, b: 4} to form a word, what is the expected number of matches of the pattern 'gb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 4, t: 2, l: 4} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 5, f: 5}. What is the expected number of occurrences of the pattern 'fa+' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, l: 3, z: 5}, what is the expected number of times the pattern 'wz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 3, d: 4, x: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'x*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.09
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 1, i: 3, s: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'i+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, o: 3, n: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 3, r: 4, t: 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 1, r: 2, f: 1, a: 2, p: 4}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 4, q: 3, t: 3}. What is the expected number of occurrences of the pattern 't.*q' 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 5 letters from the multiset {w: 3, l: 2, m: 1, s: 4}. What is the expected number of occurrences of the pattern 'mw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {v: 6, r: 4} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, w: 2, z: 3, d: 3}. What is the expected number of occurrences of the pattern 'z+w' 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 5 letters from the multiset {z: 2, a: 1, v: 1, h: 3, l: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 3, o: 3, h: 3, d: 1} 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"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 1, k: 1, z: 3, q: 3, h: 2}, what is the expected number of times the pattern 'z+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
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