messages
listlengths 1
1
| ground_truth
stringclasses 108
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, o: 3, n: 2, g: 2, d: 1}, what is the expected number of times the pattern 'o*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, z: 2, x: 2, f: 5}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 4, t: 3, l: 5} to form a word, what is the expected number of matches of the pattern 'l.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 2, y: 3, k: 6, p: 1}. What is the expected number of occurrences of the pattern 'i.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 5, m: 7} 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"
}
] |
4.77
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 2, b: 5, t: 5} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 1, g: 2, j: 9}. What is the expected number of occurrences of the pattern 'jk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.34
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 2, r: 5, h: 1, o: 1, f: 3}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 3, u: 9}, what is the expected number of times the pattern 'u.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.07
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, t: 1, r: 5, l: 2, p: 2}. What is the expected number of occurrences of the pattern 't+k' 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 6 letters from the multiset {d: 4, m: 2, x: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 6, a: 6}, what is the expected number of times the pattern 'a*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 3, y: 4, n: 5} to form a word, what is the expected number of matches of the pattern 'yn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 4, h: 8} 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 1, g: 1, c: 4, a: 1, n: 5}, what is the expected number of times the pattern 'g*a' 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 6 by randomly selecting letters from the multiset {q: 2, l: 1, k: 4, f: 2, j: 3}, what is the expected number of times the pattern 'j*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 4, m: 2, z: 6} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 4, c: 3, n: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.08
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 1, d: 2, y: 3, u: 5, i: 1}, what is the expected number of times the pattern 'yu+' appears? 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 6 by randomly selecting letters from the multiset {u: 2, n: 4, d: 2, j: 2, g: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 2, d: 1, p: 4, i: 5} to form a word, what is the expected number of matches of the pattern 'p.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.91
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 8, o: 4} to form a word, what is the expected number of matches of the pattern 'a*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 3, s: 3, p: 1, n: 5}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {l: 2, h: 2, c: 4, u: 3, a: 1}. What is the expected number of occurrences of the pattern 'l*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 3, k: 3, q: 6} to form a word, what is the expected number of matches of the pattern 'q*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.57
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 6, t: 3, n: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 4, j: 6, u: 2}, what is the expected number of times the pattern 'j+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.71
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, j: 7}. What is the expected number of occurrences of the pattern 'j.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.98
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, b: 2, l: 2, f: 5}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 2, x: 3, s: 5, n: 2}, 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 7, g: 5} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.77
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 4, r: 8} to form a word, what is the expected number of matches of the pattern 'rq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.56
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 1, d: 6, e: 5}, what is the expected number of times the pattern 'dt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, a: 5, w: 4}, what is the expected number of times the pattern 'da*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.3
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, z: 2, w: 2, d: 2, n: 3}, what is the expected number of times the pattern 'z.*e' appears? 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 6 by randomly selecting letters from the multiset {k: 2, d: 3, w: 3, z: 4}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 2, u: 2, h: 2, f: 3, z: 3} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 4, v: 2, t: 1, n: 5}. What is the expected number of occurrences of the pattern 'ns+' 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": "When randomly selecting 6 letters from the multiset {a: 3, j: 1, w: 6, q: 2} to form a word, what is the expected number of matches of the pattern 'aj+'? 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 6 letters from the multiset {i: 4, q: 8}. What is the expected number of occurrences of the pattern 'qi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.56
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {t: 3, i: 1, c: 4, p: 2, o: 2} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 1, y: 2, a: 4, m: 1, e: 4}. What is the expected number of occurrences of the pattern 'a+m' 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 6 letters from the multiset {m: 4, a: 8} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.56
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, n: 4, x: 3, t: 2}, what is the expected number of times the pattern 'n+t' 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 6 letters from the multiset {k: 1, c: 5, f: 2, r: 4} 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, m: 3, d: 4}. What is the expected number of occurrences of the pattern 'm*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 6, z: 3, g: 3}. What is the expected number of occurrences of the pattern 'gz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 5, n: 4, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 5, b: 7}, 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, k: 6, s: 3}. What is the expected number of occurrences of the pattern 'k+t' 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": "When randomly selecting 6 letters from the multiset {r: 1, t: 4, d: 7} to form a word, what is the expected number of matches of the pattern 'r+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.15
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 3, i: 4, r: 1, k: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {g: 4, d: 1, r: 3, y: 2, b: 2}. What is the expected number of occurrences of the pattern 'g+d' 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 6 letters from the multiset {g: 6, w: 6}. What is the expected number of occurrences of the pattern 'gw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, e: 2, m: 6}, 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 2, z: 2, c: 8} to form a word, what is the expected number of matches of the pattern 'z.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.82
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {j: 4, g: 2, h: 2, w: 2, l: 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"
}
] |
0.45
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 5, c: 3, s: 4} to form a word, what is the expected number of matches of the pattern 'ps+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.97
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 2, p: 3, d: 2, v: 3, f: 2} 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"
}
] |
1.16
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {z: 6, y: 6} to form a word, what is the expected number of matches of the pattern 'yz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.14
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, h: 3, r: 6}. What is the expected number of occurrences of the pattern 'o+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 3, e: 3, o: 3, n: 3}. 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"
}
] |
1.9
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 2, p: 3, e: 4, l: 3}. What is the expected number of occurrences of the pattern 'el*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.53
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 5, d: 3, j: 4}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 3, k: 1, a: 3, u: 4, j: 1}, what is the expected number of times the pattern 's+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 4, w: 5, i: 2, r: 1}. What is the expected number of occurrences of the pattern 'i.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, f: 2, a: 4, q: 3}, what is the expected number of times the pattern 'q*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 2, o: 5, c: 4, x: 1}, what is the expected number of times the pattern 'e*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 5, y: 2, h: 5} 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"
}
] |
2.84
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, u: 3, r: 1, l: 4, z: 1}. What is the expected number of occurrences of the pattern 'zu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.63
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {j: 2, n: 2, b: 2, a: 3, e: 3}. What is the expected number of occurrences of the pattern 'na*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 1, z: 1, q: 4, b: 2, c: 4}, what is the expected number of times the pattern 'z*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.08
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 3, j: 9}, what is the expected number of times the pattern 'j.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.07
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 3, x: 6, o: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 6, q: 6} to form a word, what is the expected number of matches of the pattern 'qa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 4, z: 3, w: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'f+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 5, q: 7}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 4, h: 2, t: 4, n: 2}, what is the expected number of times the pattern 'x+n' 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 6 letters from the multiset {m: 5, d: 1, z: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'u+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 5, g: 7} 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"
}
] |
6.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 1, n: 4, z: 4, a: 3}, 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"
}
] |
0.45
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, q: 3, h: 3, b: 3}. What is the expected number of occurrences of the pattern 'hh+' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 1, i: 2, v: 1, t: 5, l: 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": "When randomly selecting 6 letters from the multiset {z: 3, k: 9} to form a word, what is the expected number of matches of the pattern 'k+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, g: 5, j: 4}. What is the expected number of occurrences of the pattern 'g*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.3
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 6, v: 4, k: 2}, what is the expected number of times the pattern 'u*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.71
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 6, y: 6}, what is the expected number of times the pattern 'u*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 8, e: 4} to form a word, what is the expected number of matches of the pattern 'ee*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.53
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 5, g: 3, l: 4} to form a word, what is the expected number of matches of the pattern 'l*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.47
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 9, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 5, r: 5, i: 2} to form a word, what is the expected number of matches of the pattern 'i*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.91
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 5, a: 4, c: 3}. What is the expected number of occurrences of the pattern 'ci+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 6, t: 6} to form a word, what is the expected number of matches of the pattern 't.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.09
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 4, j: 4, y: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'y+j'? Round 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 6 letters from the multiset {b: 3, l: 4, t: 2, s: 2, f: 1}. What is the expected number of occurrences of the pattern 'f*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.15
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 2, e: 6, q: 4} to form a word, what is the expected number of matches of the pattern 'o*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.49
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 2, b: 4, m: 6}, what is the expected number of times the pattern 'ee+' 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 6 letters from the multiset {u: 6, b: 3, z: 3}. What is the expected number of occurrences of the pattern 'zb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 4, q: 8} to form a word, what is the expected number of matches of the pattern 'eq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, i: 2, h: 6, u: 1}. What is the expected number of occurrences of the pattern 'i*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
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