messages
listlengths 1
1
| ground_truth
stringclasses 108
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 5, m: 7} to form a word, what is the expected number of matches of the pattern 'mk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.88
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 2, f: 4, s: 2, z: 2, i: 2} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 2, v: 1, y: 2, z: 5, n: 2} to form a word, what is the expected number of matches of the pattern 'zy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.91
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 1, a: 3, l: 3, e: 5} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 2, t: 1, k: 2, d: 7} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 5, u: 4, p: 3}. What is the expected number of occurrences of the pattern 'p*u' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 2, s: 4, v: 3, w: 3}, what is the expected number of times the pattern 'sv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.53
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 2, f: 2, o: 2, k: 3, b: 3}, what is the expected number of times the pattern 'k*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 5, q: 2, w: 2, u: 3}. What is the expected number of occurrences of the pattern 'cw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, m: 9}. What is the expected number of occurrences of the pattern 'x+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.2
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 4, w: 4, i: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'h*w'? 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 {y: 8, t: 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"
}
] |
6.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 1, x: 3, r: 4, i: 2, d: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 5, r: 7}, what is the expected number of times the pattern 'rc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.37
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 2, e: 3, c: 2, r: 3, q: 2}. What is the expected number of occurrences of the pattern 'ec+' 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": "Form a word by randomly choosing 6 letters from the multiset {k: 3, h: 4, x: 2, q: 2, j: 1}. What is the expected number of occurrences of the pattern 'k.*q' 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 {q: 4, p: 2, c: 3, n: 3}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 5, x: 7} to form a word, what is the expected number of matches of the pattern 'xg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.37
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 5, v: 1, r: 3, k: 3}, what is the expected number of times the pattern 'kt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.3
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, z: 3, k: 2, i: 1, d: 3}. What is the expected number of occurrences of the pattern 'k.*z' 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": "When randomly selecting 6 letters from the multiset {b: 3, u: 9} to form a word, what is the expected number of matches of the pattern 'u+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.32
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, m: 2, a: 4, e: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 5, l: 2, z: 5} to form a word, what is the expected number of matches of the pattern 'zl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.91
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 2, l: 5, u: 2, g: 3}, what is the expected number of times the pattern 'sl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 8, u: 4} to form a word, what is the expected number of matches of the pattern 'du*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.56
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {w: 3, g: 1, t: 3, l: 5}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer 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, w: 9}. 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"
}
] |
8.18
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, p: 4, f: 4}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 4, q: 3, y: 2, o: 3} 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 5, b: 3, a: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {w: 5, v: 7}. What is the expected number of occurrences of the pattern 'w.*v' 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": "Form a word by randomly choosing 6 letters from the multiset {e: 2, z: 3, t: 3, d: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.02
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 7, j: 5}. What is the expected number of occurrences of the pattern 'j.*q' 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": "When randomly selecting 6 letters from the multiset {n: 7, o: 5} 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"
}
] |
4.77
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {v: 6, t: 6} to form a word, what is the expected number of matches of the pattern 'v+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.14
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 2, e: 2, k: 3, b: 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 8, c: 2, s: 2}. What is the expected number of occurrences of the pattern 'ps*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.65
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 3, o: 2, d: 4, r: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 2, h: 2, w: 4, k: 2, e: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, d: 2, q: 6, b: 1}. 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"
}
] |
3.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 8, t: 4}, what is the expected number of times the pattern 'y.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.64
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, w: 5, j: 4}, what is the expected number of times the pattern 'c*w' appears? Round 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 {u: 5, y: 4, d: 2, z: 1}. 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, e: 3, m: 4}, 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"
}
] |
0.58
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 2, v: 1, k: 4, o: 3, x: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 1, x: 2, w: 4, i: 3, y: 2}, what is the expected number of times the pattern 'w.*g' 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 {z: 2, o: 6, c: 4}. What is the expected number of occurrences of the pattern 'o*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.43
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 5, v: 7} to form a word, what is the expected number of matches of the pattern 'v*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 3, t: 5, s: 2, m: 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"
}
] |
2.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 3, c: 3, j: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'kc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.53
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 3, g: 3, h: 4, j: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'h+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 1, f: 1, y: 4, u: 3, k: 3}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 7, z: 5}. What is the expected number of occurrences of the pattern 'zm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 2, f: 3, i: 3, u: 4}, what is the expected number of times the pattern 'w+f' 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 6 letters from the multiset {k: 4, t: 2, d: 1, q: 3, g: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 1, s: 4, a: 1, i: 3, j: 3} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 5, s: 2, m: 5}, 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 7, i: 5}. What is the expected number of occurrences of the pattern 'i*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.38
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 2, k: 6, u: 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, k: 2, y: 7}. What is the expected number of occurrences of the pattern 'q.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 4, s: 5, l: 1, r: 2}. What is the expected number of occurrences of the pattern 'l*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.69
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 7, m: 5}, what is the expected number of times the pattern 'm.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, l: 3, k: 3, n: 3}. What is the expected number of occurrences of the pattern 'k.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.02
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 5, m: 4, l: 3}. What is the expected number of occurrences of the pattern 'lc*' 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": "When randomly selecting 6 letters from the multiset {u: 6, v: 6} to form a word, what is the expected number of matches of the pattern 'u+v'? 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 {b: 2, e: 6, p: 3, r: 1}. What is the expected number of occurrences of the pattern 'p+r' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 1, s: 5, c: 2, i: 2, r: 2}, what is the expected number of times the pattern 'r+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, l: 6, m: 4}. What is the expected number of occurrences of the pattern 'l.*b' in each word? Round your answer 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 {g: 6, n: 6}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, s: 7, t: 3}. What is the expected number of occurrences of the pattern 't*b' 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": "When randomly selecting 6 letters from the multiset {t: 4, r: 2, l: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'lt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.08
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 2, m: 4, b: 2, l: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'o+m'? 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 6 by randomly selecting letters from the multiset {h: 3, x: 5, c: 4}, 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"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 2, f: 3, j: 1, w: 3, r: 3}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 3, f: 5, w: 4} to form a word, what is the expected number of matches of the pattern 'w+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 6, o: 6}, what is the expected number of times the pattern 'zo*' appears? Round 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 {p: 2, c: 1, t: 6, l: 3}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 2, r: 3, e: 6, q: 1}, what is the expected number of times the pattern 'e*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.57
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, b: 1, c: 3, g: 3, r: 3}. What is the expected number of occurrences of the pattern 'r+g' 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 {b: 6, l: 6}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer 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 {i: 3, s: 3, v: 3, u: 3}, what is the expected number of times the pattern 'v.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.02
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 4, u: 1, w: 2, z: 1, k: 4}, what is the expected number of times the pattern 'k.*k' appears? 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 {h: 4, t: 2, e: 3, d: 3}. What is the expected number of occurrences of the pattern 'he*' 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": "When randomly selecting 6 letters from the multiset {g: 5, n: 2, f: 5} to form a word, what is the expected number of matches of the pattern 'g.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.14
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 2, p: 1, n: 3, c: 1, w: 5}, what is the expected number of times the pattern 'wp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.69
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 2, s: 5, d: 3, 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"
}
] |
0.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 1, r: 2, c: 3, w: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'l.*w'? Round 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 {m: 7, s: 5}. What is the expected number of occurrences of the pattern 's+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.88
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 7, u: 5} to form a word, what is the expected number of matches of the pattern 's.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 3, f: 6, p: 3}. What is the expected number of occurrences of the pattern 'n.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.02
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, h: 5, i: 4}, what is the expected number of times the pattern 'h*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.3
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 7, y: 5} to form a word, what is the expected number of matches of the pattern 'ry+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.88
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 3, l: 9} to form a word, what is the expected number of matches of the pattern 'a.*l'? 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 {x: 1, j: 4, l: 3, t: 3, n: 1}, what is the expected number of times the pattern 'nl+' 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 6 letters from the multiset {b: 3, h: 3, g: 6}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 4, x: 5, h: 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 4, m: 5, e: 2, r: 1}. What is the expected number of occurrences of the pattern 'p.*m' in each word? Round your answer 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 {m: 1, p: 4, i: 2, o: 1, a: 4}. What is the expected number of occurrences of the pattern 'o.*o' 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 {y: 7, v: 5}, what is the expected number of times the pattern 'y*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {v: 5, b: 7}. What is the expected number of occurrences of the pattern 'vv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.47
|
MATH
|
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 3