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combinatory_pattern_matching_train_0200
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, h: 3, s: 1, p: 1}, 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}" } ]
0.0
math
combinatory_pattern_matching_train_0201
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, m: 3, n: 1}, what is the expected number of times the pattern 'm+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.25
math
combinatory_pattern_matching_train_0202
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, q: 1, t: 1, j: 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}" } ]
0.08
math
combinatory_pattern_matching_train_0203
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, p: 1, r: 1, f: 2}, what is the expected number of times the pattern 'p+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0204
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, h: 1, m: 1, n: 1}. What is the expected number of occurrences of the pattern 'm.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.25
math
combinatory_pattern_matching_train_0205
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, a: 2}. What is the expected number of occurrences of the pattern 'h+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.17
math
combinatory_pattern_matching_train_0206
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, w: 1, j: 2, z: 2}. What is the expected number of occurrences of the pattern 'j.*z' 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_0207
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, z: 2, k: 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}" } ]
0.6
math
combinatory_pattern_matching_train_0208
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, y: 2, x: 2}, what is the expected number of times the pattern 'fx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.3
math
combinatory_pattern_matching_train_0209
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {s: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'rs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.93
math
combinatory_pattern_matching_train_0210
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, x: 4}, what is the expected number of times the pattern 'x.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0211
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {l: 3, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0212
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {r: 3, h: 1}. 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_0213
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 2, y: 1, p: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0214
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {x: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'fx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.5
math
combinatory_pattern_matching_train_0215
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {w: 4, q: 2} 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}" } ]
0.2
math
combinatory_pattern_matching_train_0216
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {e: 2, a: 2}. What is the expected number of occurrences of the pattern 'ae+' 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_0217
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {d: 1, e: 2, i: 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}" } ]
0.17
math
combinatory_pattern_matching_train_0218
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, m: 1, n: 1, t: 2, h: 1}. What is the expected number of occurrences of the pattern 'ht*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.65
math
combinatory_pattern_matching_train_0219
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, h: 3}. What is the expected number of occurrences of the pattern 'ph+' 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_0220
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {c: 3, y: 2}. What is the expected number of occurrences of the pattern 'yc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.1
math
combinatory_pattern_matching_train_0221
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, p: 3}, what is the expected number of times the pattern 'p*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.0
math
combinatory_pattern_matching_train_0222
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, p: 4}. What is the expected number of occurrences of the pattern 'p+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.73
math
combinatory_pattern_matching_train_0223
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {j: 2, t: 1, e: 2, x: 1}. What is the expected number of occurrences of the pattern 'je*' 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_0224
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 3, b: 1}, what is the expected number of times the pattern 'kk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.0
math
combinatory_pattern_matching_train_0225
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {v: 1, u: 1, f: 2, b: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'v+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.03
math
combinatory_pattern_matching_train_0226
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, c: 2, f: 1}, what is the expected number of times the pattern 'c.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0227
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {c: 2, j: 1, i: 1, l: 1}. What is the expected number of occurrences of the pattern 'li+' 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_0228
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {e: 1, r: 1, o: 1, i: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'i.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0229
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, w: 1, j: 2}, what is the expected number of times the pattern 'w.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.25
math
combinatory_pattern_matching_train_0230
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, y: 1, i: 1, n: 1, v: 1}, 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}" } ]
0.1
math
combinatory_pattern_matching_train_0231
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, x: 2, a: 1, n: 1, z: 1}, what is the expected number of times the pattern 'xz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0232
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, c: 1, t: 1, d: 1, b: 1}, what is the expected number of times the pattern 'cd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.57
math
combinatory_pattern_matching_train_0233
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, x: 3}, what is the expected number of times the pattern 'xf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0234
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {v: 2, p: 1, d: 1, u: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'dv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0235
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, z: 2, s: 1, k: 1}, what is the expected number of times the pattern 'ks+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0236
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 4, l: 2}, what is the expected number of times the pattern 'ly*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.93
math
combinatory_pattern_matching_train_0237
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, e: 1, n: 2, y: 1, h: 1}. What is the expected number of occurrences of the pattern 'x*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.57
math
combinatory_pattern_matching_train_0238
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 3, k: 2}, what is the expected number of times the pattern 'k+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0239
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, r: 2, f: 1, z: 1}, what is the expected number of times the pattern 'zh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.65
math
combinatory_pattern_matching_train_0240
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {l: 3, m: 1, w: 1}. What is the expected number of occurrences of the pattern 'l.*m' 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_0241
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 1, h: 1, w: 1}, what is the expected number of times the pattern 'wx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.92
math
combinatory_pattern_matching_train_0242
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, u: 1, e: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.9
math
combinatory_pattern_matching_train_0243
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {v: 1, a: 2, w: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'v*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.13
math
combinatory_pattern_matching_train_0244
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, e: 1, p: 1, b: 1, r: 1}, what is the expected number of times the pattern 'p.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.05
math
combinatory_pattern_matching_train_0245
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {f: 1, z: 1, w: 1, n: 1, g: 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}" } ]
0.05
math
combinatory_pattern_matching_train_0246
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, k: 3}, what is the expected number of times the pattern 'q.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.25
math
combinatory_pattern_matching_train_0247
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, s: 2, w: 1}. What is the expected number of occurrences of the pattern 'c*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.17
math
combinatory_pattern_matching_train_0248
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, q: 2, h: 2}, what is the expected number of times the pattern 'qh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.3
math
combinatory_pattern_matching_train_0249
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {h: 3, z: 3}. 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}" } ]
0.2
math
combinatory_pattern_matching_train_0250
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {t: 3, c: 1} to form a word, what is the expected number of matches of the pattern 't*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.75
math
combinatory_pattern_matching_train_0251
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {g: 1, f: 1, n: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.92
math
combinatory_pattern_matching_train_0252
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, i: 4}, 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}" } ]
0.0
math
combinatory_pattern_matching_train_0253
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 2, g: 2, z: 1, i: 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}" } ]
0.07
math
combinatory_pattern_matching_train_0254
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {h: 2, w: 4} 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}" } ]
1.2
math
combinatory_pattern_matching_train_0255
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {x: 1, d: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'd.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.08
math
combinatory_pattern_matching_train_0256
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, o: 1}, what is the expected number of times the pattern 'o+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
math
combinatory_pattern_matching_train_0257
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, r: 2, y: 2}. What is the expected number of occurrences of the pattern 'd*y' 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_0258
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, n: 1}. What is the expected number of occurrences of the pattern 'no*' 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_0259
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {l: 3, f: 3}. What is the expected number of occurrences of the pattern 'fl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.3
math
combinatory_pattern_matching_train_0260
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {n: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'xn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.25
math
combinatory_pattern_matching_train_0261
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {a: 1, m: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.9
math
combinatory_pattern_matching_train_0262
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, c: 1, l: 2}, what is the expected number of times the pattern 'l+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.15
math
combinatory_pattern_matching_train_0263
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {a: 2, g: 1, e: 1, i: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.37
math
combinatory_pattern_matching_train_0264
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, y: 1, d: 2, f: 1}. What is the expected number of occurrences of the pattern 'd.*r' 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_0265
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {p: 2, z: 1, h: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0266
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {k: 2, r: 1, l: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'il+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.13
math
combinatory_pattern_matching_train_0267
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, z: 1, o: 1, n: 1, p: 2}. What is the expected number of occurrences of the pattern 'n+c' 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_0268
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, k: 1, y: 1, j: 1, s: 1}, what is the expected number of times the pattern 'vk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.05
math
combinatory_pattern_matching_train_0269
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {d: 2, c: 1, h: 1, z: 2}. What is the expected number of occurrences of the pattern 'hz*' 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_0270
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {j: 3, e: 3}. What is the expected number of occurrences of the pattern 'e.*j' 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_0271
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, z: 1, m: 1}, 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}" } ]
0.0
math
combinatory_pattern_matching_train_0272
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {a: 2, b: 3}. 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}" } ]
0.1
math
combinatory_pattern_matching_train_0273
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {q: 1, i: 2, d: 3} 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}" } ]
0.6
math
combinatory_pattern_matching_train_0274
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {p: 2, z: 1, y: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0275
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, n: 1, d: 1, p: 1, r: 1}. 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}" } ]
0.0
math
combinatory_pattern_matching_train_0276
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, l: 1, m: 1, t: 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_0277
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {n: 2, b: 1, l: 1, c: 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_0278
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, c: 1, h: 1, g: 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}" } ]
0.0
math
combinatory_pattern_matching_train_0279
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {y: 2, e: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'y+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0280
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {r: 2, f: 1, i: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0281
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, j: 1, h: 1, t: 1, y: 1}, what is the expected number of times the pattern 'yq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.7
math
combinatory_pattern_matching_train_0282
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, r: 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}" } ]
0.3
math
combinatory_pattern_matching_train_0283
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, f: 2, u: 3}, what is the expected number of times the pattern 'f.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0284
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, h: 1, o: 1, s: 2, z: 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}" } ]
0.37
math
combinatory_pattern_matching_train_0285
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {p: 1, z: 1, q: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0286
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 1, 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}" } ]
0.5
math
combinatory_pattern_matching_train_0287
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, s: 4}. What is the expected number of occurrences of the pattern 's.*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_0288
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 2 letters from the multiset {r: 2, c: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'k+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0289
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, t: 1, j: 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}" } ]
0.0
math
combinatory_pattern_matching_train_0290
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {l: 2, g: 1, y: 3}. 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}" } ]
0.07
math
combinatory_pattern_matching_train_0291
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 2 letters from the multiset {l: 1, n: 2, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' 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_0292
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, b: 1, j: 1, l: 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}" } ]
0.0
math
combinatory_pattern_matching_train_0293
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, c: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0294
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, r: 2}. What is the expected number of occurrences of the pattern 'rd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.0
math
combinatory_pattern_matching_train_0295
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, b: 3}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.4
math
combinatory_pattern_matching_train_0296
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, z: 1, x: 2}, what is the expected number of times the pattern 'x.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0297
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, q: 1, d: 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_0298
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, y: 1, h: 1, q: 1}. What is the expected number of occurrences of the pattern 'y+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.17
math
combinatory_pattern_matching_train_0299
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, c: 1, a: 1, s: 2, j: 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}" } ]
0.0
math