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combinatory_pattern_matching_train_0800
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {i: 1, y: 1, a: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'j+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.28
math
combinatory_pattern_matching_train_0801
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, e: 1, j: 1, w: 1, y: 1}, what is the expected number of times the pattern 'yw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0802
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 4, y: 2}, what is the expected number of times the pattern 'y.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.6
math
combinatory_pattern_matching_train_0803
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, s: 1, i: 4, t: 2}, what is the expected number of times the pattern 'st*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.45
math
combinatory_pattern_matching_train_0804
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, c: 3, o: 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_0805
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {a: 3, f: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'f.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.43
math
combinatory_pattern_matching_train_0806
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {o: 1, l: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'ov+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.23
math
combinatory_pattern_matching_train_0807
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, v: 2, j: 1, q: 1, c: 1}, what is the expected number of times the pattern 'qc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0808
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {e: 1, v: 2, o: 1, t: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'vb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.82
math
combinatory_pattern_matching_train_0809
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, a: 4, m: 2}. What is the expected number of occurrences of the pattern 'au+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.48
math
combinatory_pattern_matching_train_0810
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 3, d: 3}. What is the expected number of occurrences of the pattern 'k*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.0
math
combinatory_pattern_matching_train_0811
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, w: 4}. 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}" } ]
2.4
math
combinatory_pattern_matching_train_0812
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 2, a: 1, d: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0813
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {i: 1, y: 2, t: 1, f: 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}" } ]
0.2
math
combinatory_pattern_matching_train_0814
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {r: 1, m: 1, x: 1, e: 1, j: 4} 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}" } ]
1.29
math
combinatory_pattern_matching_train_0815
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, i: 1, c: 2, r: 2, d: 2}. What is the expected number of occurrences of the pattern 'm+d' 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_0816
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {s: 1, b: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'sh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0817
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, i: 2, q: 1, g: 2}, what is the expected number of times the pattern 'q.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0818
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {f: 4, m: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'fn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.48
math
combinatory_pattern_matching_train_0819
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {k: 3, h: 2, p: 3} 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}" } ]
0.32
math
combinatory_pattern_matching_train_0820
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {n: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'h*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3.0
math
combinatory_pattern_matching_train_0821
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, x: 5}, what is the expected number of times the pattern 't+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.0
math
combinatory_pattern_matching_train_0822
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {u: 5, o: 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}" } ]
0.64
math
combinatory_pattern_matching_train_0823
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {y: 2, f: 1, c: 3} 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}" } ]
0.4
math
combinatory_pattern_matching_train_0824
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, p: 2, w: 1}. What is the expected number of occurrences of the pattern 'p*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.13
math
combinatory_pattern_matching_train_0825
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, n: 2, i: 1, t: 1, u: 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}" } ]
0.21
math
combinatory_pattern_matching_train_0826
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {c: 1, f: 1, w: 2, b: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'cf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.64
math
combinatory_pattern_matching_train_0827
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, v: 1, m: 2, g: 3}, 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}" } ]
0.21
math
combinatory_pattern_matching_train_0828
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {p: 2, w: 1, g: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.43
math
combinatory_pattern_matching_train_0829
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, c: 4}, what is the expected number of times the pattern 'cz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.93
math
combinatory_pattern_matching_train_0830
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, a: 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}" } ]
0.86
math
combinatory_pattern_matching_train_0831
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, z: 3, i: 2}. What is the expected number of occurrences of the pattern 'i+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.23
math
combinatory_pattern_matching_train_0832
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {i: 2, b: 1, s: 1, y: 2, z: 1}. 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}" } ]
0.73
math
combinatory_pattern_matching_train_0833
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {k: 2, a: 1, z: 3, j: 1, y: 1}. What is the expected number of occurrences of the pattern 'za*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.66
math
combinatory_pattern_matching_train_0834
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, q: 4}, what is the expected number of times the pattern 'q.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.8
math
combinatory_pattern_matching_train_0835
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {j: 3, c: 1, z: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'jq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.11
math
combinatory_pattern_matching_train_0836
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {e: 5, 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}" } ]
0.64
math
combinatory_pattern_matching_train_0837
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, d: 2, v: 2, m: 2, z: 1}, what is the expected number of times the pattern 'd.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0838
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, o: 2, m: 2}. What is the expected number of occurrences of the pattern 'g.*m' 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_0839
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {v: 2, t: 1, q: 2, s: 1, n: 1} to form a word, what is the expected number of matches of the pattern 's+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0840
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, m: 3, h: 1}, what is the expected number of times the pattern 'r.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0841
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, n: 5}. What is the expected number of occurrences of the pattern 'sn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.52
math
combinatory_pattern_matching_train_0842
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {y: 2, r: 1, g: 1, i: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'r*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.29
math
combinatory_pattern_matching_train_0843
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {a: 1, l: 1, x: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'lx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0844
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, b: 1, p: 1, h: 2, a: 1}, what is the expected number of times the pattern 'hh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.13
math
combinatory_pattern_matching_train_0845
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, k: 1, s: 4}. What is the expected number of occurrences of the pattern 's.*k' 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_0846
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 3, o: 1, f: 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_0847
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {v: 3, c: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'v+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.56
math
combinatory_pattern_matching_train_0848
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {t: 3, i: 1, n: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'n*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.43
math
combinatory_pattern_matching_train_0849
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, y: 5}. What is the expected number of occurrences of the pattern 'yo*' 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_0850
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, x: 2, d: 1, l: 4}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.64
math
combinatory_pattern_matching_train_0851
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, n: 2, h: 1, i: 1, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0852
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 3, d: 3, q: 1}, what is the expected number of times the pattern 'qd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.28
math
combinatory_pattern_matching_train_0853
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {z: 3, d: 1, q: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
math
combinatory_pattern_matching_train_0854
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, n: 4}. 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}" } ]
1.71
math
combinatory_pattern_matching_train_0855
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {b: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'z*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.67
math
combinatory_pattern_matching_train_0856
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {b: 3, z: 5} 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}" } ]
0.64
math
combinatory_pattern_matching_train_0857
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {w: 4, l: 3}. What is the expected number of occurrences of the pattern 'l+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.11
math
combinatory_pattern_matching_train_0858
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, u: 1, m: 1, v: 2, j: 2}. What is the expected number of occurrences of the pattern 'i*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.48
math
combinatory_pattern_matching_train_0859
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {y: 2, z: 1, l: 4, t: 1} to form a word, what is the expected number of matches of the pattern 'z+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0860
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, k: 2, w: 1, f: 1, x: 2}. What is the expected number of occurrences of the pattern 'w+x' 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_0861
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {f: 3, j: 5}. What is the expected number of occurrences of the pattern 'f.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.61
math
combinatory_pattern_matching_train_0862
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {u: 5, y: 2}. What is the expected number of occurrences of the pattern 'y.*u' 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_0863
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, x: 1, r: 1, d: 1}. 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_0864
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {x: 1, f: 1, n: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'xf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.77
math
combinatory_pattern_matching_train_0865
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, h: 3, s: 2}. What is the expected number of occurrences of the pattern 'h*v' 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_0866
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {w: 3, u: 5} to form a word, what is the expected number of matches of the pattern 'wu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.27
math
combinatory_pattern_matching_train_0867
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {k: 2, w: 2, r: 1, i: 2, d: 1} 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}" } ]
0.11
math
combinatory_pattern_matching_train_0868
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {a: 1, d: 1, m: 2, p: 2, x: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0869
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, x: 2, v: 2}, 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}" } ]
0.07
math
combinatory_pattern_matching_train_0870
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, b: 4}. What is the expected number of occurrences of the pattern 'k*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.0
math
combinatory_pattern_matching_train_0871
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {h: 1, f: 6} to form a word, what is the expected number of matches of the pattern 'h.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0872
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {s: 2, h: 1, e: 1, t: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.53
math
combinatory_pattern_matching_train_0873
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {p: 1, c: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.43
math
combinatory_pattern_matching_train_0874
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {a: 1, k: 6, o: 1} to form a word, what is the expected number of matches of the pattern 'ka+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0875
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {f: 2, a: 2, l: 2, n: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0876
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {w: 2, h: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'u+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.36
math
combinatory_pattern_matching_train_0877
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, n: 2, s: 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}" } ]
0.32
math
combinatory_pattern_matching_train_0878
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {f: 2, q: 1, a: 1, w: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'qa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0879
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {i: 2, d: 1, r: 2, e: 1}. What is the expected number of occurrences of the pattern 'i+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.23
math
combinatory_pattern_matching_train_0880
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, p: 1, i: 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}" } ]
1.13
math
combinatory_pattern_matching_train_0881
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {q: 1, g: 1, k: 1, o: 2, s: 2}. What is the expected number of occurrences of the pattern 'k.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.29
math
combinatory_pattern_matching_train_0882
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {r: 2, p: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'r*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.36
math
combinatory_pattern_matching_train_0883
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {a: 4, m: 4} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
math
combinatory_pattern_matching_train_0884
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, x: 2, w: 1, b: 1, j: 1}. What is the expected number of occurrences of the pattern 'p*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.53
math
combinatory_pattern_matching_train_0885
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, o: 3, g: 1, r: 1}, what is the expected number of times the pattern 'ov*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.2
math
combinatory_pattern_matching_train_0886
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {k: 2, p: 2, j: 1, n: 3} 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}" } ]
0.21
math
combinatory_pattern_matching_train_0887
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 3, g: 1, m: 2, i: 2}, 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}" } ]
0.21
math
combinatory_pattern_matching_train_0888
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, h: 3, f: 1, l: 1}, what is the expected number of times the pattern 'f*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.41
math
combinatory_pattern_matching_train_0889
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {u: 3, f: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'f*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.07
math
combinatory_pattern_matching_train_0890
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, i: 1, m: 2, n: 1, q: 1}, what is the expected number of times the pattern 'm.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.29
math
combinatory_pattern_matching_train_0891
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, w: 2, x: 1, v: 1}, 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}" } ]
0.0
math
combinatory_pattern_matching_train_0892
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, w: 1, r: 2, c: 2}. 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}" } ]
0.29
math
combinatory_pattern_matching_train_0893
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, u: 2, q: 1}. What is the expected number of occurrences of the pattern 'r*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.35
math
combinatory_pattern_matching_train_0894
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 1, v: 1, p: 1, x: 2}, what is the expected number of times the pattern 'rx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.15
math
combinatory_pattern_matching_train_0895
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {g: 2, m: 1, i: 1, c: 4} to form a word, what is the expected number of matches of the pattern 'c+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0896
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {k: 1, j: 4, f: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0897
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, f: 4, a: 2, p: 1}, what is the expected number of times the pattern 'a*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.45
math
combinatory_pattern_matching_train_0898
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {g: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
math
combinatory_pattern_matching_train_0899
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {y: 1, t: 1, p: 3, r: 2}. What is the expected number of occurrences of the pattern 'tr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.73
math