messages
listlengths 1
1
| ground_truth
stringclasses 65
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 2, c: 2, y: 1, o: 4} to form a word, what is the expected number of matches of the pattern 'l+c'? 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, w: 3, d: 2}. What is the expected number of occurrences of the pattern 'de*' 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 {t: 3, m: 4, d: 1, q: 1}. What is the expected number of occurrences of the pattern 't+m' in each word? Round your answer 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 {r: 2, k: 2, w: 3, d: 2}, what is the expected number of times the pattern 'd*r' 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, j: 5} to form a word, what is the expected number of matches of the pattern 'j.*j'? 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 {w: 2, a: 1, m: 2, p: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? 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 {j: 2, w: 3, i: 1, y: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, g: 3, m: 4}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 4, w: 1, j: 1, t: 2, u: 1}, what is the expected number of times the pattern 'j*t' 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 {q: 1, o: 3, y: 4, e: 1} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 2, v: 3, c: 2, b: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'c*u'? 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 {x: 1, o: 3, k: 2, f: 2, c: 1}. What is the expected number of occurrences of the pattern 'ck*' 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 {q: 1, e: 1, i: 1, p: 3, v: 3} to form a word, what is the expected number of matches of the pattern 've+'? 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 {k: 5, j: 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 {z: 1, t: 3, a: 3, q: 2}. 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, s: 2, h: 2, l: 4}. What is the expected number of occurrences of the pattern 'el*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 2, v: 7}. What is the expected number of occurrences of the pattern 'e*v' in each word? Round your answer 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 {f: 2, y: 3, e: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'y.*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 {m: 1, l: 4, i: 2, t: 2}. What is the expected number of occurrences of the pattern 'lm*' in each word? Round your answer 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 {f: 1, p: 2, c: 2, b: 4}. 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": "Form a word by randomly choosing 4 letters from the multiset {m: 1, i: 3, h: 1, n: 2, r: 2}. What is the expected number of occurrences of the pattern 'i+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 3, n: 3, o: 2, c: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 2, g: 4, n: 3} to form a word, what is the expected number of matches of the pattern 'n*g'? 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 {x: 3, c: 3, i: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'ix*'? 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 {s: 1, a: 2, f: 1, m: 3, b: 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"
}
] |
0.08
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, u: 3, a: 3}, what is the expected number of times the pattern 'u*a' appears? Round 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 {q: 2, k: 3, c: 1, e: 2, b: 1}, 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"
}
] |
0.09
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 5, z: 4}, what is the expected number of times the pattern 'zd+' appears? 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 {b: 1, j: 1, a: 3, o: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'gg+'? 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 {b: 1, y: 1, v: 2, k: 3, n: 2}. What is the expected number of occurrences of the pattern 'v.*b' 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 {v: 3, p: 1, o: 2, e: 3}. What is the expected number of occurrences of the pattern 'e+p' 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 {w: 6, f: 3}, what is the expected number of times the pattern 'wf+' 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 {m: 3, q: 2, p: 1, v: 3}. What is the expected number of occurrences of the pattern 'qv*' 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: 2, o: 3, a: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'a.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 2, a: 5, t: 2}. What is the expected number of occurrences of the pattern 't+a' 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 {h: 2, u: 7} 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"
}
] |
3.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 3, m: 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"
}
] |
2.14
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 4, t: 2, 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 3, z: 1, r: 3, j: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? 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 {y: 1, l: 1, w: 1, m: 3, a: 3}, what is the expected number of times the pattern 'am+' 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 4 letters from the multiset {k: 4, q: 5}. What is the expected number of occurrences of the pattern 'q+k' 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 {f: 3, v: 2, m: 4}, what is the expected number of times the pattern 'vm+' appears? 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 {i: 3, v: 3, r: 3}. What is the expected number of occurrences of the pattern 'r.*i' 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": "When randomly selecting 4 letters from the multiset {p: 2, y: 1, h: 3, q: 3} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 3, k: 1, w: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'k*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.46
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 5, e: 4}. What is the expected number of occurrences of the pattern 'o*e' 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 {g: 1, t: 3, x: 1, k: 4}, what is the expected number of times the pattern 'g+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.13
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 3, d: 2, t: 4} to form a word, what is the expected number of matches of the pattern 'd*v'? 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 {y: 1, c: 2, w: 4, t: 2}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, u: 4, d: 3}. What is the expected number of occurrences of the pattern 'o+d' 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 {v: 3, g: 2, f: 1, q: 2, w: 1} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {m: 7, v: 2}. What is the expected number of occurrences of the pattern 'mv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.75
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 5, q: 3, f: 1}, what is the expected number of times the pattern 'f.*f' 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 {q: 2, a: 3, u: 2, i: 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
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 6, a: 3}. What is the expected number of occurrences of the pattern 'u+a' 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 {g: 3, j: 4, r: 2}, what is the expected number of times the pattern 'jg*' 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 {n: 1, q: 2, y: 1, e: 3, x: 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": "Form a word by randomly choosing 4 letters from the multiset {q: 4, d: 5}. What is the expected number of occurrences of the pattern 'dq*' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 6, f: 3}, what is the expected number of times the pattern 'f.*g' appears? Round 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 {y: 2, e: 3, x: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'yx+'? Round 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 {k: 2, f: 1, y: 3, x: 2, v: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {w: 1, s: 2, b: 2, v: 4} 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": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 7, o: 2}, what is the expected number of times the pattern 'j.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 1, h: 1, q: 1, d: 3, f: 3} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, x: 6}, what is the expected number of times the pattern 'w+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 2, b: 1, m: 2, k: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? 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 {a: 2, k: 4, l: 2, r: 1}. What is the expected number of occurrences of the pattern 'r*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.97
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 1, h: 3, w: 5} to form a word, what is the expected number of matches of the pattern 'we+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.21
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, m: 7}. What is the expected number of occurrences of the pattern 'm*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.94
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 1, h: 1, w: 2, o: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'w.*g'? 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 {u: 6, e: 3}, 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"
}
] |
3.57
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 8, g: 1}, what is the expected number of times the pattern 'sg+' 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 {q: 3, b: 2, l: 2, f: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'q+b'? Round 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 {k: 6, d: 3} to form a word, what is the expected number of matches of the pattern 'kd*'? 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 {e: 6, f: 3}, what is the expected number of times the pattern 'f.*f' 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 {c: 1, p: 3, q: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'y+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.13
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 3, x: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 5, f: 4} to form a word, what is the expected number of matches of the pattern 'fa*'? 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 {p: 2, f: 3, t: 4}. What is the expected number of occurrences of the pattern 'tp+' 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 {h: 5, v: 4}, what is the expected number of times the pattern 'hv+' 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 {h: 4, f: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'f.*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: 3, s: 2, c: 4}, what is the expected number of times the pattern 'c+s' appears? 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 {c: 4, g: 2, i: 3}. What is the expected number of occurrences of the pattern 'g*i' 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 {y: 3, r: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'r*y'? 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 {z: 4, g: 5}. What is the expected number of occurrences of the pattern 'z.*g' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 1, u: 2, d: 3, k: 3}, what is the expected number of times the pattern 'd.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.75
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 6, f: 3} 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"
}
] |
1.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, r: 3, i: 2}, what is the expected number of times the pattern 'i.*i' 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 {t: 5, s: 4}. 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"
}
] |
1.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, s: 2, l: 2, r: 2}. 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"
}
] |
0.18
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 1, p: 1, r: 1, z: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? 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: 1, f: 2, b: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'mg+'? 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 {m: 3, e: 2, s: 1, x: 1, j: 2}. What is the expected number of occurrences of the pattern 'sx+' 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": "When randomly selecting 4 letters from the multiset {c: 4, r: 5} to form a word, what is the expected number of matches of the pattern 'cr*'? 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 {r: 1, y: 3, x: 4, v: 1}. What is the expected number of occurrences of the pattern 'yr+' 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": "When randomly selecting 4 letters from the multiset {y: 2, c: 5, w: 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": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, i: 3, w: 3, l: 1}, what is the expected number of times the pattern 'lw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.15
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 4, y: 5}. 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"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {o: 2, c: 2, a: 2, m: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'mo+'? 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: 4, a: 5}. 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"
}
] |
1.11
|
MATH
|
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