messages
listlengths 1
1
| ground_truth
stringclasses 65
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 1, j: 2, c: 2, d: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'de*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.97
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 2, o: 4, c: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'eo+'? 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 {v: 2, g: 2, n: 5}. What is the expected number of occurrences of the pattern 'v+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.46
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {w: 3, r: 2, s: 4} 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"
}
] |
1.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 3, a: 1, l: 4, r: 1} to form a word, what is the expected number of matches of the pattern 'lr*'? Round 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 {u: 2, c: 1, j: 2, w: 2, n: 2}, what is the expected number of times the pattern 'n.*c' 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 {q: 5, w: 4} to form a word, what is the expected number of matches of the pattern 'q.*q'? 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 4 by randomly selecting letters from the multiset {a: 4, k: 4, i: 1}, what is the expected number of times the pattern 'a+i' 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 {x: 2, h: 2, l: 2, w: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'l*x'? 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 {c: 3, t: 1, k: 2, s: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, q: 3, i: 4}. What is the expected number of occurrences of the pattern 'iu+' in each word? Round your answer 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 {c: 2, y: 7} to form a word, what is the expected number of matches of the pattern 'cy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.94
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, m: 2, n: 3, u: 2}. What is the expected number of occurrences of the pattern 'mn*' 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 4 by randomly selecting letters from the multiset {h: 5, y: 4}, 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"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 6, s: 3}, what is the expected number of times the pattern 's+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 3, k: 2, l: 3, f: 1}. What is the expected number of occurrences of the pattern 'l.*r' 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: 1, j: 3, t: 2, i: 2, s: 1}, what is the expected number of times the pattern 's+j' 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 4 letters from the multiset {a: 4, n: 5}. 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"
}
] |
1.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 1, p: 1, a: 1, o: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'a*k'? Round 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 {e: 1, c: 3, r: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'i*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.61
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, w: 3, t: 1, m: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, h: 3, l: 4}, what is the expected number of times the pattern 'l*v' 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 4 by randomly selecting letters from the multiset {l: 4, r: 3, p: 2}, what is the expected number of times the pattern 'p.*l' 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 {k: 4, d: 3, w: 2}, what is the expected number of times the pattern 'w.*k' 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 4 letters from the multiset {o: 2, g: 2, u: 1, p: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'pg+'? Round 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 {i: 3, v: 2, m: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'ip*'? 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 {y: 2, d: 1, q: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? 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 {d: 6, v: 3} to form a word, what is the expected number of matches of the pattern 'v+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, q: 4, e: 3}. What is the expected number of occurrences of the pattern 'q.*e' 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 {q: 4, o: 5}, what is the expected number of times the pattern 'q.*o' 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 4 by randomly selecting letters from the multiset {i: 1, f: 3, m: 3, x: 2}, what is the expected number of times the pattern 'ix+' 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 {l: 7, i: 2}, what is the expected number of times the pattern 'i*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.75
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 2, c: 2, u: 1, r: 3, a: 1} to form a word, what is the expected number of matches of the pattern 'u+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.04
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 2, y: 2, m: 1, x: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'mu*'? 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 {y: 4, n: 1, r: 2, 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": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 3, v: 6}, what is the expected number of times the pattern 'v.*k' 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 {l: 4, u: 5}, what is the expected number of times the pattern 'l+u' 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 {o: 1, l: 2, g: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'o+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 2, t: 1, j: 1, k: 3, s: 2} to form a word, what is the expected number of matches of the pattern 't+v'? 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: 2, n: 2, t: 1, v: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 3, w: 6}, what is the expected number of times the pattern 'w+u' appears? 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 {w: 2, l: 2, o: 1, b: 2, u: 2}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 1, p: 2, a: 2, j: 1, i: 3}. What is the expected number of occurrences of the pattern 'p+j' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, m: 2, d: 3, e: 2}, 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {n: 4, s: 1, m: 2, y: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? 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 {m: 2, r: 2, t: 3, q: 2}. What is the expected number of occurrences of the pattern 'm*t' 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 {v: 4, f: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? 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 {n: 4, w: 3, m: 2}. What is the expected number of occurrences of the pattern 'm+n' in each word? Round your answer 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 {q: 2, s: 2, p: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*s'? 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 {p: 2, b: 1, y: 5, n: 1}. What is the expected number of occurrences of the pattern 'p+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.46
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, o: 7}, 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"
}
] |
1.94
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 4, e: 5}, what is the expected number of times the pattern 'm*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.33
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, a: 4, m: 1, o: 2}, what is the expected number of times the pattern 'a.*m' appears? Round 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 {s: 2, l: 5, t: 2} to form a word, what is the expected number of matches of the pattern 't+s'? Round 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 4 by randomly selecting letters from the multiset {q: 2, a: 7}, 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"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 3, b: 1, p: 3, h: 2}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 4, y: 5}, what is the expected number of times the pattern 'yz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.11
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 5, p: 2, b: 2}, what is the expected number of times the pattern 'p*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.97
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 3, w: 6} to form a word, what is the expected number of matches of the pattern 'w.*h'? 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 {q: 2, p: 2, g: 2, i: 2, x: 1}, what is the expected number of times the pattern 'gq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 4, d: 5} to form a word, what is the expected number of matches of the pattern 'd+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 {b: 1, x: 1, q: 3, s: 2, l: 2}. What is the expected number of occurrences of the pattern 'q+x' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 5, b: 4}, what is the expected number of times the pattern 'n.*b' 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 4 letters from the multiset {b: 2, p: 7}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 3, d: 3, m: 3}. What is the expected number of occurrences of the pattern 'd*r' 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 4 by randomly selecting letters from the multiset {r: 3, d: 1, w: 5}, what is the expected number of times the pattern 'dr*' 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 {x: 4, u: 3, d: 2}. What is the expected number of occurrences of the pattern 'd+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 {c: 3, m: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'c.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {n: 1, x: 2, d: 3, u: 1, v: 2}. What is the expected number of occurrences of the pattern 'n+d' 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": "Form a word by randomly choosing 4 letters from the multiset {x: 1, s: 1, k: 5, d: 2}. What is the expected number of occurrences of the pattern 'k*x' 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": "Form a word by randomly choosing 4 letters from the multiset {t: 4, l: 1, n: 1, a: 2, p: 1}. What is the expected number of occurrences of the pattern 't.*n' 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 {k: 2, e: 1, f: 1, a: 3, w: 2}. What is the expected number of occurrences of the pattern 'a+k' 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 {e: 2, k: 2, v: 1, y: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'v.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.08
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, z: 3, o: 4}, 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 {z: 4, j: 5}, what is the expected number of times the pattern 'j+z' appears? 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 {k: 3, s: 3, n: 1, l: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, u: 5, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 4, y: 2, q: 2, n: 1} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 5, d: 4}. What is the expected number of occurrences of the pattern 'd+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.11
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {n: 3, m: 6}. What is the expected number of occurrences of the pattern 'm.*n' 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 4 letters from the multiset {a: 5, i: 4}. What is the expected number of occurrences of the pattern 'i*a' 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 4 letters from the multiset {d: 3, w: 2, j: 2, g: 2}. What is the expected number of occurrences of the pattern 'w.*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": "When randomly selecting 4 letters from the multiset {i: 2, v: 5, b: 2} 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, u: 3, n: 1, c: 4}. What is the expected number of occurrences of the pattern 'wn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.04
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 6, z: 3}. 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": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 1, b: 3, y: 2, z: 1, o: 2}, 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"
}
] |
0.25
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 7, j: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, r: 1, w: 2, c: 1, j: 3}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 4, z: 5} 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"
}
] |
3.01
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 4, d: 3, c: 2}, 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, s: 1, e: 2, g: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, j: 3, f: 3, c: 1}, what is the expected number of times the pattern 'c.*t' 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 {q: 2, m: 1, w: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'qm+'? 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 {y: 3, h: 2, v: 1, c: 1, g: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 7, l: 2}, what is the expected number of times the pattern 'v.*l' appears? Round 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 {i: 1, x: 3, k: 1, g: 3, z: 1}, what is the expected number of times the pattern 'g.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 4, m: 5} to form a word, what is the expected number of matches of the pattern 'im*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {m: 5, o: 4}. What is the expected number of occurrences of the pattern 'mo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.11
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, a: 1, q: 3, u: 3}. What is the expected number of occurrences of the pattern 'lu*' 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": "When randomly selecting 4 letters from the multiset {y: 1, j: 2, n: 1, a: 3, g: 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"
}
] |
0.5
|
MATH
|
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