messages
listlengths 1
1
| ground_truth
stringclasses 65
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 5, f: 2, w: 1, g: 1}. What is the expected number of occurrences of the pattern 'v+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.31
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 6, l: 3} to form a word, what is the expected number of matches of the pattern 'm+l'? 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 {c: 4, y: 3, z: 2}. What is the expected number of occurrences of the pattern 'cz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.14
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, n: 5}, 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"
}
] |
1.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 2, d: 5, v: 2}, what is the expected number of times the pattern 'ov*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 5, r: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, p: 1, q: 6}. What is the expected number of occurrences of the pattern 'o+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.55
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 2, v: 2, x: 2, d: 2, b: 1}. What is the expected number of occurrences of the pattern 'xb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.08
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, v: 5}, what is the expected number of times the pattern 'd*v' 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 4 letters from the multiset {m: 2, o: 3, p: 4} to form a word, what is the expected number of matches of the pattern 'm+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.37
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 3, r: 4, w: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 5, m: 4} to form a word, what is the expected number of matches of the pattern 'm*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.33
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 2, m: 1, f: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'fm+'? 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 {z: 2, l: 3, c: 4}. 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"
}
] |
1.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, q: 3, d: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 3, j: 2, w: 2, x: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'w.*r'? 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 {d: 2, w: 3, k: 2, z: 2}, what is the expected number of times the pattern 'k*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.61
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 6, w: 3} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 2, g: 5, x: 2} to form a word, what is the expected number of matches of the pattern 'x*y'? 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 {t: 1, q: 2, e: 2, g: 3, p: 1} 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {y: 2, g: 2, n: 2, l: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, e: 5, i: 1}, what is the expected number of times the pattern 'ez*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.98
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {o: 4, b: 1, f: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'f+b'? Round 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 4 letters from the multiset {k: 5, y: 4}. 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"
}
] |
1.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 2, i: 1, u: 3, k: 1, x: 2}. 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, q: 1, e: 4}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, l: 4, n: 3}. What is the expected number of occurrences of the pattern 'x+n' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, r: 1, a: 5, p: 1}, what is the expected number of times the pattern 'p*r' appears? Round 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 4 by randomly selecting letters from the multiset {x: 6, k: 3}, what is the expected number of times the pattern 'k+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, v: 2, t: 3, w: 2}. 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 6, u: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 2, c: 4, v: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'f+v'? Round 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 4 letters from the multiset {u: 2, d: 1, s: 4, e: 2}. What is the expected number of occurrences of the pattern 'e+s' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, l: 2, z: 1, n: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 2, u: 3, o: 4} to form a word, what is the expected number of matches of the pattern 'or+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.37
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 7, b: 2}, 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"
}
] |
3.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, q: 2, s: 1, o: 3}, 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"
}
] |
1.61
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 1, i: 1, r: 2, g: 5} 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"
}
] |
0.97
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, x: 1, m: 2, v: 2, h: 1}. What is the expected number of occurrences of the pattern 'v.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 3, s: 2, k: 4}, what is the expected number of times the pattern 'hk+' 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 4 letters from the multiset {h: 2, a: 2, i: 1, q: 2, o: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 5, a: 3, j: 1}, what is the expected number of times the pattern 'q.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.25
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 2, e: 2, c: 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"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 2, a: 2, u: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'ca+'? 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 {v: 4, a: 5}, what is the expected number of times the pattern 'va*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 6, y: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 2, l: 7} to form a word, what is the expected number of matches of the pattern 'lh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, z: 3, a: 2}. What is the expected number of occurrences of the pattern 'j*a' 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": "When randomly selecting 4 letters from the multiset {d: 2, c: 1, s: 3, n: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 3, s: 3, h: 1, m: 1, f: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, u: 2, q: 5}, what is the expected number of times the pattern 'u.*u' 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 {u: 3, e: 2, m: 2, i: 2} 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 3, g: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'yg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.61
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, d: 1, u: 1, c: 3, n: 1}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, i: 2, z: 4, m: 1}, what is the expected number of times the pattern 'i+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.37
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 6, y: 3}, what is the expected number of times the pattern 'yl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.56
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 6, i: 3}, what is the expected number of times the pattern 'hi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.57
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 2, q: 1, a: 2, x: 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"
}
] |
1.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 4, t: 5}. What is the expected number of occurrences of the pattern 'tl*' 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 {g: 1, m: 3, c: 2, f: 2, i: 1}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 3, d: 3, m: 3}. 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"
}
] |
0.75
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, f: 2, s: 2, u: 1, o: 2}, what is the expected number of times the pattern 'l+s' appears? 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 {h: 1, m: 2, p: 2, l: 2, s: 2}, what is the expected number of times the pattern 'hs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, m: 2, j: 3, g: 2}, what is the expected number of times the pattern 'n+m' appears? Round 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 4 letters from the multiset {e: 4, o: 2, y: 3}. What is the expected number of occurrences of the pattern 'y+o' 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": "Form a word by randomly choosing 4 letters from the multiset {l: 5, s: 4}. What is the expected number of occurrences of the pattern 'sl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.23
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 4, e: 5}, what is the expected number of times the pattern 'we*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 3, f: 2, j: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'c+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, z: 3, d: 3, s: 2}. What is the expected number of occurrences of the pattern 'sd+' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 6, h: 3}, what is the expected number of times the pattern 'eh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.57
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, u: 3, t: 3}, what is the expected number of times the pattern 'u.*u' 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 {o: 1, v: 2, e: 2, i: 1, u: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 2, h: 2, b: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'z.*b'? 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 4 by randomly selecting letters from the multiset {n: 2, f: 2, b: 2, u: 3}, what is the expected number of times the pattern 'u*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 5, c: 4} to form a word, what is the expected number of matches of the pattern 'u.*c'? 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 {i: 2, n: 3, b: 4}. 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 4, f: 5} to form a word, what is the expected number of matches of the pattern 'f*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 2, t: 3, g: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'tz+'? 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 {i: 3, k: 3, j: 1, s: 2}. What is the expected number of occurrences of the pattern 's*k' 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": "Form a word by randomly choosing 4 letters from the multiset {b: 5, c: 2, m: 2}. What is the expected number of occurrences of the pattern 'c.*m' 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 {r: 3, m: 2, h: 1, k: 3}. What is the expected number of occurrences of the pattern 'm*k' 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 {d: 1, h: 3, p: 5} to form a word, what is the expected number of matches of the pattern 'd.*d'? 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 {j: 3, e: 4, z: 2}. What is the expected number of occurrences of the pattern 'e*z' 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 4 letters from the multiset {g: 7, m: 2}. What is the expected number of occurrences of the pattern 'g.*g' 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": "When randomly selecting 4 letters from the multiset {l: 3, w: 2, i: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'u*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 6, m: 3}, what is the expected number of times the pattern 'ma*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.56
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 3, b: 2, m: 2, j: 1, n: 1} to form a word, what is the expected number of matches of the pattern 's+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.15
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 3, a: 3, h: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'a+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.45
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 2, i: 2, r: 1, d: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'm*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 3, h: 3, s: 3}. What is the expected number of occurrences of the pattern 's.*s' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 4, l: 5}, what is the expected number of times the pattern 'wl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.23
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, z: 1, i: 4, u: 2}, what is the expected number of times the pattern 'i*u' 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 {h: 4, y: 2, o: 3}, what is the expected number of times the pattern 'yh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.44
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 1, p: 3, s: 2, t: 2, o: 1}, what is the expected number of times the pattern 't.*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 {s: 5, y: 4} 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"
}
] |
1.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 5, c: 4} 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"
}
] |
1.23
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 5, g: 4} 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"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, s: 1, b: 2, j: 1, k: 1}, what is the expected number of times the pattern 'k+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.04
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, d: 6}, what is the expected number of times the pattern 'd*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.56
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 2, w: 3, m: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'w+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.15
|
MATH
|
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