messages
listlengths 1
1
| ground_truth
stringclasses 85
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 3, w: 2, f: 2, r: 2, o: 1}. What is the expected number of occurrences of the pattern 'w+f' 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": "When randomly selecting 5 letters from the multiset {p: 5, i: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'wp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.5
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, d: 1, i: 2, n: 2, h: 2}, 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"
}
] |
0.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 2, f: 4, c: 4}, what is the expected number of times the pattern 'cf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.95
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {i: 3, u: 3, e: 2, k: 2}. 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 4, i: 1, l: 2, p: 3} 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 1, a: 3, n: 2, i: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'an*'? 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: 5, q: 5} to form a word, what is the expected number of matches of the pattern 'qj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.17
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 6, f: 4}, what is the expected number of times the pattern 'fo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 3, z: 4, w: 3} to form a word, what is the expected number of matches of the pattern 'w+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.64
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 7, q: 3}. What is the expected number of occurrences of the pattern 'q.*q' 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 {u: 3, a: 3, i: 2, j: 2}. What is the expected number of occurrences of the pattern 'ua*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, b: 3, n: 2, k: 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"
}
] |
1.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 7, q: 3}. What is the expected number of occurrences of the pattern 'q.*q' 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 {p: 2, x: 4, f: 2, a: 2}. What is the expected number of occurrences of the pattern 'pf*' 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 {s: 3, f: 5, v: 2}, what is the expected number of times the pattern 'sv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.29
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 1, f: 6, d: 3}, what is the expected number of times the pattern 'ed*' appears? 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 {a: 3, o: 2, x: 2, z: 3}. What is the expected number of occurrences of the pattern 'a*x' in each word? Round your answer 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 5 by randomly selecting letters from the multiset {q: 5, a: 5}, 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"
}
] |
2.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 1, i: 2, z: 2, p: 3, v: 2}, what is the expected number of times the pattern 'pv*' appears? Round 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 {w: 4, i: 6}, what is the expected number of times the pattern 'wi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 7, y: 3}. What is the expected number of occurrences of the pattern 'd+y' 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 {v: 4, t: 3, o: 1, p: 2}, what is the expected number of times the pattern 'po*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 2, t: 3, n: 5}. What is the expected number of occurrences of the pattern 'n*a' 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 {b: 5, j: 5}, what is the expected number of times the pattern 'jb+' appears? 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 {j: 3, q: 7}, 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"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 3, t: 1, u: 2, k: 2, q: 2}, 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, a: 8}. What is the expected number of occurrences of the pattern 's+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.78
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, e: 2, p: 3, l: 1}, what is the expected number of times the pattern 'el+' 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 {z: 4, o: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'zo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.95
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 2, w: 2, e: 5, k: 1}. What is the expected number of occurrences of the pattern 'w+w' 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": "When randomly selecting 5 letters from the multiset {y: 4, d: 2, e: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? 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 {d: 3, r: 1, l: 4, w: 2} 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"
}
] |
2.21
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 2, t: 3, x: 3, j: 2}, 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"
}
] |
0.29
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 4, c: 2, l: 2, q: 2} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 2, e: 8}. What is the expected number of occurrences of the pattern 'eo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.78
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 4, c: 6}, what is the expected number of times the pattern 'hc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 1, u: 4, t: 2, x: 2, r: 1}. What is the expected number of occurrences of the pattern 'up+' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 2, p: 8}, 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"
}
] |
6.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, z: 2, u: 3, q: 3}. What is the expected number of occurrences of the pattern 'u+q' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 5, v: 1, n: 1, p: 2, f: 1}, what is the expected number of times the pattern 'n.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.11
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 6, t: 4} to form a word, what is the expected number of matches of the pattern 'tg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 2, o: 1, w: 4, m: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'ow+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.24
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {t: 6, v: 4} to form a word, what is the expected number of matches of the pattern 'v+t'? 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 {f: 4, y: 6}, what is the expected number of times the pattern 'f+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 2, v: 3, o: 2, i: 1, c: 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"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 4, d: 6}, what is the expected number of times the pattern 'dc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 2, z: 4, a: 4}. 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"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 4, t: 6}, what is the expected number of times the pattern 'rt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 5, e: 5}, what is the expected number of times the pattern 'n+e' 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 {s: 5, d: 5} to form a word, what is the expected number of matches of the pattern 'd.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.78
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {t: 2, f: 3, n: 5} to form a word, what is the expected number of matches of the pattern 't+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.29
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 2, h: 3, u: 1, p: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'pz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, c: 9}. What is the expected number of occurrences of the pattern 'c*d' 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": "Form a word by randomly choosing 5 letters from the multiset {m: 2, j: 5, k: 3}. 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 1, m: 1, e: 1, s: 3, a: 4}. What is the expected number of occurrences of the pattern 'e+a' 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": "Form a word by randomly choosing 5 letters from the multiset {u: 3, d: 6, h: 1}. What is the expected number of occurrences of the pattern 'h.*d' 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 {h: 4, l: 2, c: 2, s: 2}. What is the expected number of occurrences of the pattern 'l.*c' in each word? Round your answer 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 5 letters from the multiset {u: 3, g: 7}. 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": "When randomly selecting 5 letters from the multiset {y: 1, w: 4, m: 5} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 3, b: 2, y: 2, v: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'n.*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 {p: 7, s: 3}, what is the expected number of times the pattern 'sp*' appears? Round 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 {u: 1, b: 3, n: 4, m: 2}. What is the expected number of occurrences of the pattern 'u*b' in each word? Round your answer 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 {m: 4, d: 6}. What is the expected number of occurrences of the pattern 'm.*d' 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 {m: 2, k: 3, d: 5}. What is the expected number of occurrences of the pattern 'd*m' 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 5 letters from the multiset {z: 6, d: 4} to form a word, what is the expected number of matches of the pattern 'd+z'? 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: 2, a: 7, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 5, s: 5}. 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"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 2, m: 1, d: 3, x: 2, l: 2}. What is the expected number of occurrences of the pattern 'mx*' 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": "When randomly selecting 5 letters from the multiset {t: 4, d: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'd+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 3, h: 5, q: 2}, what is the expected number of times the pattern 'h.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 2, q: 4, e: 2, n: 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 2, w: 2, h: 2, d: 1, i: 3} to form a word, what is the expected number of matches of the pattern 'iw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.29
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 1, b: 3, i: 5, z: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? 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 5 by randomly selecting letters from the multiset {p: 2, i: 3, w: 3, n: 2}, 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 2, s: 3, i: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'i+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, t: 4, c: 1, o: 2}, what is the expected number of times the pattern 'om+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 4, b: 6}, 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"
}
] |
0.64
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 7, t: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {v: 3, z: 4, e: 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"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 1, t: 2, h: 2, w: 3, d: 2}, what is the expected number of times the pattern 'w.*h' 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 {m: 2, k: 3, h: 5}. What is the expected number of occurrences of the pattern 'm+h' 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 5 by randomly selecting letters from the multiset {x: 4, o: 6}, 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"
}
] |
3.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 2, r: 2, z: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'ra*'? 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 {y: 3, p: 1, c: 1, b: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'c.*y'? 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 {e: 1, d: 4, a: 3, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {u: 3, x: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'xu*'? 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 {q: 3, b: 2, j: 1, p: 4}, what is the expected number of times the pattern 'j.*b' 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 {b: 2, f: 2, d: 4, s: 2}, what is the expected number of times the pattern 'f+d' 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 {c: 5, k: 5} 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"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {r: 5, j: 2, q: 3}. What is the expected number of occurrences of the pattern 'q*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 5, u: 5} to form a word, what is the expected number of matches of the pattern 'o.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.78
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 2, v: 3, i: 2, s: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'si+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.19
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 4, y: 6} to form a word, what is the expected number of matches of the pattern 'y.*d'? 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 5 letters from the multiset {h: 1, f: 1, m: 4, o: 2, i: 2}. What is the expected number of occurrences of the pattern 'o+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 4, w: 6}, what is the expected number of times the pattern 'w+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 4, u: 2, b: 4} 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"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 3, a: 3, x: 2, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 2, e: 2, c: 2, i: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'ec+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.19
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, o: 2, h: 3, z: 3}, what is the expected number of times the pattern 'o*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.