messages
listlengths 1
1
| ground_truth
stringclasses 65
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, x: 5}, what is the expected number of times the pattern 'x+t' 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 {p: 3, a: 2, x: 2, i: 2}. What is the expected number of occurrences of the pattern 'i+x' 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 4 by randomly selecting letters from the multiset {l: 3, o: 6}, what is the expected number of times the pattern 'l*o' 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 {d: 2, t: 2, m: 2, l: 1, c: 2}, what is the expected number of times the pattern 'tc+' 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 {c: 2, z: 4, a: 2, m: 1}, what is the expected number of times the pattern 'cm+' appears? 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 {a: 3, h: 2, k: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'a.*h'? 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 {l: 3, h: 6}. What is the expected number of occurrences of the pattern 'h.*l' 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": "When randomly selecting 4 letters from the multiset {r: 1, j: 2, h: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, q: 3, u: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 4, c: 4, m: 1} 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"
}
] |
1.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 2, b: 2, p: 2, z: 3} to form a word, what is the expected number of matches of the pattern 'lb+'? 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 {t: 6, b: 2, c: 1}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, v: 3, e: 2, s: 1}, what is the expected number of times the pattern 'se*' 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 {p: 1, w: 4, u: 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"
}
] |
1.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 3, t: 3, u: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 2, s: 4, k: 3} to form a word, what is the expected number of matches of the pattern 's*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.38
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 1, c: 2, h: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'c*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.14
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 2, h: 1, i: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'ma+'? 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 {i: 3, s: 4, q: 2}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 2, o: 2, f: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'fs*'? 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 {a: 8, k: 1}. What is the expected number of occurrences of the pattern 'k.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 3, s: 3, r: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, x: 3, j: 2}, what is the expected number of times the pattern 'tx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.38
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, h: 5}. What is the expected number of occurrences of the pattern 'jh+' 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 {u: 1, h: 2, y: 2, a: 1, s: 3}, 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, a: 2, f: 1, x: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 1, j: 2, s: 2, z: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'j*z'? 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 {n: 3, v: 6} to form a word, what is the expected number of matches of the pattern 'n.*v'? Round 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 {g: 4, z: 5}. 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"
}
] |
3.01
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 4, n: 3, g: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 5, v: 4}. What is the expected number of occurrences of the pattern 'v.*e' 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 4 letters from the multiset {c: 2, b: 2, q: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'c*p'? 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 {e: 3, p: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'e.*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 {m: 2, n: 2, j: 5} to form a word, what is the expected number of matches of the pattern 'mj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.62
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 3, d: 3, c: 3} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, q: 3, n: 3, r: 2}. What is the expected number of occurrences of the pattern 'r+q' 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 {u: 4, y: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'y+u'? 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: 1, a: 3, p: 2, h: 3}. What is the expected number of occurrences of the pattern 'xp+' 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 4 letters from the multiset {k: 4, i: 2, v: 1, a: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'i+a'? 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 {b: 1, j: 1, z: 3, q: 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"
}
] |
0.49
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, f: 3, l: 4}, what is the expected number of times the pattern 'f.*l' appears? 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 {y: 3, h: 1, a: 1, k: 1, f: 3}. What is the expected number of occurrences of the pattern 'y.*y' 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 {p: 3, v: 6} to form a word, what is the expected number of matches of the pattern 'v*p'? 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 {g: 2, d: 1, p: 4, v: 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"
}
] |
0.37
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 2, u: 2, x: 2, v: 2, f: 1}, what is the expected number of times the pattern 'f.*w' 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 {c: 4, h: 5}, 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"
}
] |
3.33
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, t: 1, m: 3, k: 1, q: 3}, what is the expected number of times the pattern 'tc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.49
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, q: 2, d: 1, g: 3}. What is the expected number of occurrences of the pattern 'k+g' 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": "Form a word by randomly choosing 4 letters from the multiset {m: 1, w: 5, e: 2, r: 1}. What is the expected number of occurrences of the pattern 'r.*m' 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 4 letters from the multiset {m: 4, o: 1, z: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 2, v: 3, z: 4} to form a word, what is the expected number of matches of the pattern 'vi+'? Round 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 {k: 3, y: 2, i: 4}, what is the expected number of times the pattern 'y*i' appears? 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 4 letters from the multiset {k: 4, z: 5}. What is the expected number of occurrences of the pattern 'kz*' in each word? Round your answer 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 {c: 7, e: 2}, what is the expected number of times the pattern 'ce+' appears? 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 4 letters from the multiset {a: 3, h: 6}. What is the expected number of occurrences of the pattern 'a.*h' 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 {r: 2, o: 7}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, f: 2, v: 2, r: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {y: 2, v: 1, g: 4, b: 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"
}
] |
1.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 3, n: 1, x: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'js+'? Round 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 {o: 4, x: 5} to form a word, what is the expected number of matches of the pattern 'o*x'? 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 {s: 3, p: 2, d: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'pd*'? 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: 1, f: 3, a: 2, w: 1, s: 2} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, a: 3, t: 4}. What is the expected number of occurrences of the pattern 'dt*' 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 {f: 3, r: 6}. What is the expected number of occurrences of the pattern 'fr+' 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 {x: 2, u: 1, c: 2, b: 1, s: 3}, what is the expected number of times the pattern 'x.*x' 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 {t: 1, k: 1, z: 3, y: 2, h: 2} 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 2, x: 1, d: 1, y: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'x*q'? 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 {p: 1, j: 3, m: 1, z: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'z.*q'? 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 {l: 6, z: 3}, what is the expected number of times the pattern 'l*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.56
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 2, k: 2, p: 2, r: 1, o: 2}. What is the expected number of occurrences of the pattern 'o*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 3, i: 3, q: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'ei*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, n: 1, t: 2, e: 3, u: 1}, what is the expected number of times the pattern 'e.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 6, f: 3}. 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 3, k: 2, w: 3, v: 1}, what is the expected number of times the pattern 'w*v' 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 {j: 1, c: 2, r: 2, x: 3, a: 1}. 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, p: 1, f: 6, l: 1}, what is the expected number of times the pattern 'l+f' 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 {v: 3, h: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'v*b'? 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 {r: 1, m: 5, l: 3}. What is the expected number of occurrences of the pattern 'm*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.26
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, s: 3, l: 2, p: 2, o: 1}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, g: 3, q: 2, k: 2}. What is the expected number of occurrences of the pattern 'kg*' 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 {t: 2, z: 7}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, k: 6}, what is the expected number of times the pattern 'vk+' 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 {i: 1, s: 2, p: 2, o: 2, w: 2}. What is the expected number of occurrences of the pattern 'w.*s' 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": "When randomly selecting 4 letters from the multiset {w: 2, x: 1, d: 3, f: 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": "When randomly selecting 4 letters from the multiset {x: 1, u: 2, c: 3, b: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 1, d: 2, u: 3, p: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, v: 2, i: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 3, u: 6} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 3, m: 1, j: 1, q: 1, l: 3}. What is the expected number of occurrences of the pattern 'm.*q' 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 {z: 2, g: 6, l: 1}, what is the expected number of times the pattern 'gl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, y: 2, l: 2, d: 1, n: 3}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 5, y: 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"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 3, d: 5, o: 1} to form a word, what is the expected number of matches of the pattern 'r.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.25
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 4, f: 3, n: 2}. What is the expected number of occurrences of the pattern 'f+n' 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 {l: 6, t: 3}, 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"
}
] |
2.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 2, e: 7} to form a word, what is the expected number of matches of the pattern 'er+'? 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 4 letters from the multiset {d: 4, s: 5}. What is the expected number of occurrences of the pattern 'd.*s' 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 4 letters from the multiset {a: 4, q: 5} 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"
}
] |
1.11
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 5, i: 4} to form a word, what is the expected number of matches of the pattern 'm+i'? 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, y: 4, p: 3}, what is the expected number of times the pattern 'yp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
MATH
|
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