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_0400
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, a: 4}. 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0401
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 1, g: 3, e: 4}. What is the expected number of occurrences of the pattern 'e.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.29
|
math
|
combinatory_pattern_matching_train_0402
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 5, k: 2}, what is the expected number of times the pattern 'c+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.24
|
math
|
combinatory_pattern_matching_train_0403
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, k: 1, q: 2, i: 1}, what is the expected number of times the pattern 'i*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.77
|
math
|
combinatory_pattern_matching_train_0404
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, l: 1, f: 1, h: 1}, what is the expected number of times the pattern 'h*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0405
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {l: 1, j: 1, h: 4, e: 1} to form a word, what is the expected number of matches of the pattern 'j*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.64
|
math
|
combinatory_pattern_matching_train_0406
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, i: 1, d: 2, o: 1}, what is the expected number of times the pattern 'd+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0407
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {j: 1, e: 3, b: 1, z: 1, n: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0408
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 1, c: 2, y: 2, m: 1, q: 1} to form a word, what is the expected number of matches of the pattern 's+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0409
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {p: 1, x: 1, r: 1, f: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'p*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.64
|
math
|
combinatory_pattern_matching_train_0410
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 3, x: 2, r: 2}. What is the expected number of occurrences of the pattern 'x+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.15
|
math
|
combinatory_pattern_matching_train_0411
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {h: 1, v: 2, i: 1, r: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'y*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0412
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {h: 1, s: 2, p: 1, z: 1, j: 1} 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}"
}
] |
0.4
|
math
|
combinatory_pattern_matching_train_0413
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, u: 3}, what is the expected number of times the pattern 'ud+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0414
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, p: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.86
|
math
|
combinatory_pattern_matching_train_0415
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, l: 1, x: 2, k: 1, b: 2}. What is the expected number of occurrences of the pattern 'x*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.62
|
math
|
combinatory_pattern_matching_train_0416
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, b: 2, i: 1, y: 2}, what is the expected number of times the pattern 'yc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.4
|
math
|
combinatory_pattern_matching_train_0417
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, q: 2, z: 1, k: 2}. What is the expected number of occurrences of the pattern 'zk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.45
|
math
|
combinatory_pattern_matching_train_0418
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, p: 2, z: 1, q: 1}, what is the expected number of times the pattern 'z.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0419
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {u: 1, i: 2, x: 1, n: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.77
|
math
|
combinatory_pattern_matching_train_0420
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 2, p: 4}. What is the expected number of occurrences of the pattern 'iu*' 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_0421
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, i: 4}. What is the expected number of occurrences of the pattern 'gi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.67
|
math
|
combinatory_pattern_matching_train_0422
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, x: 1, e: 3, o: 2}. What is the expected number of occurrences of the pattern 'rx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.64
|
math
|
combinatory_pattern_matching_train_0423
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 1, t: 1, u: 1, w: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0424
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, g: 5, n: 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}"
}
] |
2.14
|
math
|
combinatory_pattern_matching_train_0425
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, y: 4}, 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}"
}
] |
0.43
|
math
|
combinatory_pattern_matching_train_0426
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, w: 2, g: 1, a: 1}. What is the expected number of occurrences of the pattern 'g+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.13
|
math
|
combinatory_pattern_matching_train_0427
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, o: 2, d: 2, z: 2}, what is the expected number of times the pattern 'z*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0428
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, a: 2, q: 3}. What is the expected number of occurrences of the pattern 'qx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.5
|
math
|
combinatory_pattern_matching_train_0429
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, f: 2, e: 1, d: 1}. What is the expected number of occurrences of the pattern 'e+f' 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_0430
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, u: 1, n: 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0431
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, j: 2, r: 2, v: 1}, what is the expected number of times the pattern 'jv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.13
|
math
|
combinatory_pattern_matching_train_0432
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, s: 2, h: 2, m: 1}, what is the expected number of times the pattern 's+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.32
|
math
|
combinatory_pattern_matching_train_0433
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, u: 2, p: 1, f: 1, c: 3}. 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}"
}
] |
0.32
|
math
|
combinatory_pattern_matching_train_0434
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, s: 3, r: 3}, what is the expected number of times the pattern 'rs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.1
|
math
|
combinatory_pattern_matching_train_0435
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, k: 1, j: 1, l: 1, h: 1}, what is the expected number of times the pattern 'j.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0436
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, n: 1, m: 1, x: 3}. What is the expected number of occurrences of the pattern 'nx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.42
|
math
|
combinatory_pattern_matching_train_0437
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, k: 1, u: 1, j: 1, n: 2}, 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_0438
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 5, y: 3}, what is the expected number of times the pattern 'y+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.62
|
math
|
combinatory_pattern_matching_train_0439
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {n: 1, l: 3, o: 1, z: 3} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0440
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, a: 5}, what is the expected number of times the pattern 'a.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.0
|
math
|
combinatory_pattern_matching_train_0441
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 3, e: 1, z: 4}, what is the expected number of times the pattern 'ez+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0442
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {m: 2, u: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'u+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.25
|
math
|
combinatory_pattern_matching_train_0443
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, l: 1, d: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0444
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 4, z: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'yz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.11
|
math
|
combinatory_pattern_matching_train_0445
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, m: 1, j: 1, x: 3, o: 1}, what is the expected number of times the pattern 't.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.14
|
math
|
combinatory_pattern_matching_train_0446
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {s: 2, q: 1, b: 3, r: 1, c: 1} to form a word, what is the expected number of matches of the pattern 's.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0447
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, h: 3, b: 1, o: 1, j: 2}. What is the expected number of occurrences of the pattern 'lb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.55
|
math
|
combinatory_pattern_matching_train_0448
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, g: 2, e: 2, k: 1, f: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0449
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 5, m: 3}, what is the expected number of times the pattern 'mr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.84
|
math
|
combinatory_pattern_matching_train_0450
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, a: 1, y: 2, p: 1, r: 3}, what is the expected number of times the pattern 't.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0451
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, s: 2, w: 1, o: 1}. What is the expected number of occurrences of the pattern 'ow+' 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_0452
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, p: 3}. What is the expected number of occurrences of the pattern 'ep+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.25
|
math
|
combinatory_pattern_matching_train_0453
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, y: 1, z: 2, i: 1, c: 1}, what is the expected number of times the pattern 'z*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.65
|
math
|
combinatory_pattern_matching_train_0454
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 5, h: 3}, what is the expected number of times the pattern 'h+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.62
|
math
|
combinatory_pattern_matching_train_0455
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, g: 2, k: 3}, what is the expected number of times the pattern 'k.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.48
|
math
|
combinatory_pattern_matching_train_0456
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, d: 1, t: 3, l: 1}, what is the expected number of times the pattern 'dl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0457
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 1, e: 3, k: 2}. What is the expected number of occurrences of the pattern 'se*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.08
|
math
|
combinatory_pattern_matching_train_0458
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 1, k: 3, m: 2, q: 2}. What is the expected number of occurrences of the pattern 'kk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.36
|
math
|
combinatory_pattern_matching_train_0459
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 5, r: 3}. What is the expected number of occurrences of the pattern 't+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.27
|
math
|
combinatory_pattern_matching_train_0460
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, b: 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}"
}
] |
0.45
|
math
|
combinatory_pattern_matching_train_0461
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, n: 1, v: 2}, what is the expected number of times the pattern 'mv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.45
|
math
|
combinatory_pattern_matching_train_0462
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 1, t: 3, a: 2}, what is the expected number of times the pattern 'wa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.23
|
math
|
combinatory_pattern_matching_train_0463
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 4, z: 3, n: 1} 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}"
}
] |
0.32
|
math
|
combinatory_pattern_matching_train_0464
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {r: 1, e: 1, q: 1, t: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0465
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {q: 2, w: 2, i: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'q*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.24
|
math
|
combinatory_pattern_matching_train_0466
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, n: 5}. What is the expected number of occurrences of the pattern 'r.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.43
|
math
|
combinatory_pattern_matching_train_0467
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 1, a: 2, y: 1, l: 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}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0468
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {i: 2, x: 2, m: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'i.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0469
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 2, k: 1, q: 1, o: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.13
|
math
|
combinatory_pattern_matching_train_0470
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, f: 1, b: 6}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0471
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, p: 1, m: 3}, what is the expected number of times the pattern 'p+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0472
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {k: 2, s: 2, t: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'ts*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.47
|
math
|
combinatory_pattern_matching_train_0473
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, j: 2, g: 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}"
}
] |
0.43
|
math
|
combinatory_pattern_matching_train_0474
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, f: 1, z: 1, b: 2}. What is the expected number of occurrences of the pattern 'z.*z' 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_0475
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, o: 2, b: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.86
|
math
|
combinatory_pattern_matching_train_0476
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, r: 3}. What is the expected number of occurrences of the pattern 'rb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.74
|
math
|
combinatory_pattern_matching_train_0477
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, o: 1, d: 4}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0478
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, f: 2, q: 2, w: 2, h: 1}, what is the expected number of times the pattern 'hq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.62
|
math
|
combinatory_pattern_matching_train_0479
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {l: 1, w: 3, u: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'lq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0480
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 4, o: 1, x: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ya+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.14
|
math
|
combinatory_pattern_matching_train_0481
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, u: 2, j: 2}, 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}"
}
] |
0.14
|
math
|
combinatory_pattern_matching_train_0482
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, b: 2, w: 1, r: 4}, what is the expected number of times the pattern 'r.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.43
|
math
|
combinatory_pattern_matching_train_0483
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, w: 4}. What is the expected number of occurrences of the pattern 'wb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.4
|
math
|
combinatory_pattern_matching_train_0484
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, h: 1, z: 3, e: 1, r: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0485
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, t: 1, b: 1, s: 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}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0486
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, z: 2, a: 2, f: 2}, 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}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0487
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, t: 3, m: 1, z: 1}, what is the expected number of times the pattern 'z*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.64
|
math
|
combinatory_pattern_matching_train_0488
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {d: 3, q: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'q*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.93
|
math
|
combinatory_pattern_matching_train_0489
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, a: 2, f: 1, n: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0490
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, i: 3}, what is the expected number of times the pattern 'g.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0491
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, a: 1, h: 2, d: 2}, what is the expected number of times the pattern 'd.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.29
|
math
|
combinatory_pattern_matching_train_0492
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, g: 2, p: 1, b: 3}. 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}"
}
] |
0.43
|
math
|
combinatory_pattern_matching_train_0493
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, r: 2, j: 2, d: 1, o: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0494
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, y: 5}, what is the expected number of times the pattern 'y*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.84
|
math
|
combinatory_pattern_matching_train_0495
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, j: 1, f: 1, y: 1, d: 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}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0496
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {x: 3, p: 1, h: 1, k: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.11
|
math
|
combinatory_pattern_matching_train_0497
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, c: 3, i: 2}. 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}"
}
] |
0.11
|
math
|
combinatory_pattern_matching_train_0498
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 5, k: 2, e: 1}. What is the expected number of occurrences of the pattern 'ek+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.08
|
math
|
combinatory_pattern_matching_train_0499
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, j: 2, g: 1, f: 1, i: 2}, what is the expected number of times the pattern 'f+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.14
|
math
|
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