id
stringlengths 39
39
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 126
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
combinatory_pattern_matching_train_0100
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, g: 1, q: 1, l: 1}, what is the expected number of times the pattern 'k*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0101
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, l: 1, r: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0102
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {b: 1, q: 1, n: 1, l: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.7
|
math
|
combinatory_pattern_matching_train_0103
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {q: 1, o: 1, b: 1, d: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0104
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 2, w: 3}, what is the expected number of times the pattern 'w+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0105
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {t: 2, l: 1, r: 1, f: 1, q: 1}. What is the expected number of occurrences of the pattern 'rt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0106
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 1, x: 1, g: 2, l: 1}, what is the expected number of times the pattern 'x*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.45
|
math
|
combinatory_pattern_matching_train_0107
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 1, t: 1, p: 1, g: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0108
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, a: 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}"
}
] |
1.2
|
math
|
combinatory_pattern_matching_train_0109
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, o: 1}, what is the expected number of times the pattern 'z.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0110
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, g: 1, m: 1, e: 1, u: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0111
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, d: 1, g: 1, k: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0112
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, o: 3, t: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0113
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, f: 1, m: 1, n: 1, q: 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0114
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, w: 3, f: 1}, what is the expected number of times the pattern 'w.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.15
|
math
|
combinatory_pattern_matching_train_0115
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 3, x: 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0116
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, v: 1, g: 1, l: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0117
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, h: 1, x: 1, j: 1, s: 1}. What is the expected number of occurrences of the pattern 'j+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0118
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, e: 3}. What is the expected number of occurrences of the pattern 'g.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0119
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 1, w: 2, t: 1, l: 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0120
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 2, u: 1, c: 1, z: 1}. What is the expected number of occurrences of the pattern 'z+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0121
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, e: 1, m: 1, b: 1, h: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0122
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {d: 1, k: 1, o: 1, s: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'dk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0123
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {f: 2, k: 4}. What is the expected number of occurrences of the pattern 'kf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.6
|
math
|
combinatory_pattern_matching_train_0124
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {k: 1, f: 1, e: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'e.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0125
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, w: 2, y: 1}, what is the expected number of times the pattern 'w*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.17
|
math
|
combinatory_pattern_matching_train_0126
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {c: 1, v: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'uv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0127
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {f: 1, g: 1, p: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.25
|
math
|
combinatory_pattern_matching_train_0128
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, t: 1, z: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0129
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, n: 2}. What is the expected number of occurrences of the pattern 'm+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.33
|
math
|
combinatory_pattern_matching_train_0130
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {s: 1, c: 1, l: 2} to form a word, what is the expected number of matches of the pattern 's*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.17
|
math
|
combinatory_pattern_matching_train_0131
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, r: 1, i: 3}. 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0132
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, q: 3, d: 2}. 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0133
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, d: 3}, what is the expected number of times the pattern 'd*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.0
|
math
|
combinatory_pattern_matching_train_0134
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, v: 2, i: 1}. What is the expected number of occurrences of the pattern 'vi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.33
|
math
|
combinatory_pattern_matching_train_0135
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {j: 2, h: 3} to form a word, what is the expected number of matches of the pattern 'hj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.5
|
math
|
combinatory_pattern_matching_train_0136
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, n: 1, d: 1}. What is the expected number of occurrences of the pattern 'o.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
math
|
combinatory_pattern_matching_train_0137
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {s: 2, f: 1, z: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0138
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, j: 1, w: 1, o: 1, y: 2}. What is the expected number of occurrences of the pattern 'y.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0139
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, t: 1, n: 1, g: 1}, what is the expected number of times the pattern 'g*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.92
|
math
|
combinatory_pattern_matching_train_0140
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 2, x: 1, d: 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}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0141
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 2, q: 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}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0142
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {b: 3, t: 2} to form a word, what is the expected number of matches of the pattern 't+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0143
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {y: 1, l: 1, t: 1, f: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0144
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, e: 2, v: 3}, what is the expected number of times the pattern 'v+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0145
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, g: 3, l: 1}. What is the expected number of occurrences of the pattern 'fg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
math
|
combinatory_pattern_matching_train_0146
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {v: 1, z: 1, a: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'az+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0147
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, w: 1, f: 1, v: 1, z: 1}, what is the expected number of times the pattern 'w+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0148
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, x: 1, j: 1, r: 1}, what is the expected number of times the pattern 'fr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.58
|
math
|
combinatory_pattern_matching_train_0149
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, k: 3, v: 1}, 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}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0150
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, c: 4}. What is the expected number of occurrences of the pattern 'c+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0151
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, k: 2, i: 1, t: 1}, 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}"
}
] |
0.15
|
math
|
combinatory_pattern_matching_train_0152
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {y: 1, f: 2, s: 1, k: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0153
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, q: 1, l: 2, h: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0154
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {h: 2, s: 1, u: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'u+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0155
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {g: 1, q: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'gq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.92
|
math
|
combinatory_pattern_matching_train_0156
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {j: 2, y: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'j.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0157
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {h: 1, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0158
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, l: 1, a: 1, q: 2, i: 1}. 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0159
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
math
|
combinatory_pattern_matching_train_0160
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {g: 1, p: 5}. 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}"
}
] |
0.67
|
math
|
combinatory_pattern_matching_train_0161
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, c: 3}. What is the expected number of occurrences of the pattern 'c.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0162
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {q: 1, c: 2, r: 1, p: 1, n: 1}. 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0163
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, o: 1, j: 1, q: 2}. 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0164
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {u: 2, z: 1, b: 1, j: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'zb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0165
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {p: 1, i: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'p+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0166
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, y: 1, g: 1, k: 1}. What is the expected number of occurrences of the pattern 'iy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.58
|
math
|
combinatory_pattern_matching_train_0167
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, j: 2, g: 1, x: 1}. What is the expected number of occurrences of the pattern 'g.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0168
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, y: 2}. What is the expected number of occurrences of the pattern 'y+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0169
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {h: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'h+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.33
|
math
|
combinatory_pattern_matching_train_0170
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, o: 1, c: 1, x: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0171
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 3, f: 3}, what is the expected number of times the pattern 's*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.3
|
math
|
combinatory_pattern_matching_train_0172
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 1, q: 1, f: 2, d: 1}, what is the expected number of times the pattern 'c.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0173
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 2, n: 2, l: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0174
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, p: 2, e: 1, z: 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0175
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {g: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
math
|
combinatory_pattern_matching_train_0176
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {v: 2, w: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'aw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0177
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {l: 1, u: 1, q: 1, c: 1, b: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0178
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, a: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0179
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, y: 3}, 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}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0180
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, o: 2, a: 3}. What is the expected number of occurrences of the pattern 'x*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.7
|
math
|
combinatory_pattern_matching_train_0181
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, s: 2, l: 1}, what is the expected number of times the pattern 's.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0182
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, n: 1, o: 1, b: 1, q: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0183
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, l: 1, i: 2, f: 2}. What is the expected number of occurrences of the pattern 'i*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
math
|
combinatory_pattern_matching_train_0184
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, r: 1, l: 1, w: 1}. What is the expected number of occurrences of the pattern 'dr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0185
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {k: 1, j: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0186
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 2, f: 2, g: 2}. What is the expected number of occurrences of the pattern 'g*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.8
|
math
|
combinatory_pattern_matching_train_0187
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {j: 2, e: 1, q: 1, s: 1, c: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0188
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {z: 1, x: 1, v: 1, t: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'v*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.45
|
math
|
combinatory_pattern_matching_train_0189
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, f: 4, n: 1}, what is the expected number of times the pattern 'ny*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.37
|
math
|
combinatory_pattern_matching_train_0190
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, d: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0191
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {m: 2, f: 1, j: 1, n: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'ni+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0192
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {y: 1, k: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0193
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, y: 1, j: 2, w: 2}, what is the expected number of times the pattern 'jc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0194
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {p: 2, c: 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}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0195
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, j: 1, x: 1, c: 1, q: 1}, what is the expected number of times the pattern 'i*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.7
|
math
|
combinatory_pattern_matching_train_0196
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, v: 3}, what is the expected number of times the pattern 'i+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.25
|
math
|
combinatory_pattern_matching_train_0197
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, a: 1, d: 2, l: 1}, what is the expected number of times the pattern 'li*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.45
|
math
|
combinatory_pattern_matching_train_0198
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, s: 1, m: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0199
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {w: 1, k: 1, h: 1, q: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'wq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.37
|
math
|
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