messages
listlengths 1
1
| ground_truth
stringclasses 38
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, c: 1, o: 3, v: 1}, what is the expected number of times the pattern 'vc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, r: 3, g: 1}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, v: 4}. What is the expected number of occurrences of the pattern 'v+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.73
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, a: 2, q: 1, p: 1, f: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 1, q: 2, b: 1, k: 1, e: 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"
}
] |
0.13
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, t: 2, b: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, s: 2, u: 1}. 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"
}
] |
0.2
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, y: 2, r: 1, c: 1, o: 1}, what is the expected number of times the pattern 'xr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 3, z: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.13
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 2, p: 1, d: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'pr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.57
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {n: 3, h: 1, l: 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": "When randomly selecting 3 letters from the multiset {n: 2, i: 1, o: 1, x: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? 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 3 by randomly selecting letters from the multiset {o: 1, u: 1, m: 1, n: 2, c: 1}, what is the expected number of times the pattern 'om*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.57
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {i: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.25
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 5, f: 1}, what is the expected number of times the pattern 'ft*' 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 3 by randomly selecting letters from the multiset {j: 2, h: 1, w: 1, s: 1, f: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 2, h: 1, d: 1, v: 1, t: 1} 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"
}
] |
0.57
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 3, r: 1, z: 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"
}
] |
0.6
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {i: 2, a: 2, y: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'ay*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.13
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, a: 1, x: 1, g: 2}. What is the expected number of occurrences of the pattern 'xg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.65
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 1, u: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'o.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, i: 4}, 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"
}
] |
1.2
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 1, e: 2, a: 1, m: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, i: 1, c: 2, y: 1}. What is the expected number of occurrences of the pattern 'cy+' 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 3 by randomly selecting letters from the multiset {c: 4, l: 2}, what is the expected number of times the pattern 'c.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, w: 1, d: 3, a: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, w: 4}, what is the expected number of times the pattern 'ws*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.6
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 3, a: 1, u: 1}, 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"
}
] |
0.2
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, e: 3, 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": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, s: 1, q: 2, c: 1, f: 1}, what is the expected number of times the pattern 'yf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.57
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, p: 1, e: 2, v: 2}. What is the expected number of occurrences of the pattern 'p+e' 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 3 by randomly selecting letters from the multiset {u: 2, d: 1, 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"
}
] |
0.6
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, u: 3}, what is the expected number of times the pattern 'uz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.25
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 2, g: 1, v: 1, z: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'g*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.13
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, n: 2, k: 1, o: 2}, what is the expected number of times the pattern 'ek+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, h: 3}, what is the expected number of times the pattern 'h*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.25
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, h: 2}, what is the expected number of times the pattern 'th*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.6
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 2, a: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'm+a'? 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 3 letters from the multiset {r: 2, l: 1, g: 1, p: 1, s: 1}. What is the expected number of occurrences of the pattern 'p*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.57
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {l: 1, k: 2, s: 1, f: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'k.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 3, p: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, x: 1, k: 2}. What is the expected number of occurrences of the pattern 'h+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, b: 2, j: 1}. 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"
}
] |
0.2
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, r: 2, y: 2, u: 1}, what is the expected number of times the pattern 'y.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 2, i: 1, z: 1, u: 1}, what is the expected number of times the pattern 'i+w' 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 3 letters from the multiset {i: 3, j: 3}. 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"
}
] |
0.6
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 1, h: 1, a: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'h.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, n: 2, g: 1, p: 1, i: 1}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 1, r: 2, p: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, h: 4}. What is the expected number of occurrences of the pattern 'r.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, h: 1, a: 1, q: 2, g: 1}, what is the expected number of times the pattern 'az+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, s: 4, a: 1}, what is the expected number of times the pattern 'a+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 1, q: 2, m: 1, a: 1, o: 1} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'rr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.95
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, h: 4}. 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"
}
] |
1.2
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, m: 3, e: 1}. What is the expected number of occurrences of the pattern 'm+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, w: 1, e: 1, d: 1, y: 2}. What is the expected number of occurrences of the pattern 'dl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.57
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, d: 1, y: 1, q: 2}, what is the expected number of times the pattern 'd.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {e: 1, t: 2, x: 1, w: 1, p: 1} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, s: 1, d: 1, m: 1, i: 2}, what is the expected number of times the pattern 'mi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.15
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {h: 1, p: 1, f: 3, e: 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": "When randomly selecting 3 letters from the multiset {y: 1, q: 1, a: 1, w: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'y.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 5, e: 1}. What is the expected number of occurrences of the pattern 'e+t' 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 3 letters from the multiset {i: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'qi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.6
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, q: 2}. What is the expected number of occurrences of the pattern 'qo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.73
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, f: 1, c: 1, m: 2, q: 1}. What is the expected number of occurrences of the pattern 'mf+' 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 3 letters from the multiset {f: 1, o: 2, e: 1, s: 1, b: 1} to form a word, what is the expected number of matches of the pattern 's+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 2, g: 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"
}
] |
0.2
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 3, a: 1, y: 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"
}
] |
0.6
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, l: 2}. 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"
}
] |
0.2
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, z: 1, f: 2, b: 1, v: 1}. What is the expected number of occurrences of the pattern 'fv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.13
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 2, e: 1, r: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'r*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.13
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, i: 1, n: 1, h: 3}, what is the expected number of times the pattern 'n+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, a: 1, c: 2, b: 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"
}
] |
0.2
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, c: 1, j: 2, g: 1, s: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, f: 1, n: 2, s: 1}. What is the expected number of occurrences of the pattern 'a*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.65
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 1, n: 3, t: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'pn+'? 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 3 letters from the multiset {h: 1, j: 1, x: 1, o: 1, a: 2}. 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"
}
] |
0.15
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 2, u: 3}, what is the expected number of times the pattern 'o.*o' 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 3 letters from the multiset {k: 2, s: 1, q: 1, g: 1, i: 1}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 1, x: 3, n: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, q: 2, h: 2}. What is the expected number of occurrences of the pattern 'v*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.3
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'jh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.6
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {z: 2, r: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'z+r'? 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 3 letters from the multiset {k: 2, t: 4}. What is the expected number of occurrences of the pattern 't+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.73
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, h: 1, t: 2}. What is the expected number of occurrences of the pattern 'j.*t' 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 3 by randomly selecting letters from the multiset {d: 1, i: 2, j: 1, y: 1, l: 1}, 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 3 letters from the multiset {q: 2, t: 4} to form a word, what is the expected number of matches of the pattern 'qt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.73
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, n: 2, z: 1, s: 1}, what is the expected number of times the pattern 'qs+' appears? Round 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 3 by randomly selecting letters from the multiset {i: 3, z: 3}, 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"
}
] |
2.25
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 3, i: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, k: 2, n: 1, 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 3 letters from the multiset {i: 1, c: 2, j: 1, h: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 2, z: 1, u: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'zh+'? 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 3 letters from the multiset {h: 5, r: 1}. What is the expected number of occurrences of the pattern 'hr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.83
|
MATH
|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, o: 1, w: 1, k: 1, r: 1}. What is the expected number of occurrences of the pattern 'k+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.07
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, c: 2, v: 1, z: 1, p: 1}, what is the expected number of times the pattern 'vl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.57
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, g: 1, s: 1, i: 2, c: 1}, 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"
}
] |
0.2
|
MATH
|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, y: 3}, what is the expected number of times the pattern 'yv+' 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 3 letters from the multiset {l: 2, p: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'ld*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
MATH
|
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