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標題:
Random Sampling
發問:
In a hand of 15 cards drawn randomly from a deck of cards of 52, find the chance of a) no court cards (J, Q, K, A) b) at least one ace but no other court court cards c) at most one kind of court card
最佳解答:
a) P(no court card)=C(52-16,15)/C(52,15)=0.0124245 (6 sig fig) b) P(at least one ace but no other court cards) =[C(4,1)C(36,14)+C(4,2)C(36,13)+C(4,3)C(36,12)+C(4,4)C(36,11)]/C(52,15) =0.00773365 (6 sig fig) c) P(at most one kind of court card) =P(no court card)+P(exactly one court card) =0.0124245+C(5,1)C(4,1)C(36,14)/C(52,15) =0.0124245+0.0169425 =0.0293670 (6 sig fig)
Random Sampling
發問:
In a hand of 15 cards drawn randomly from a deck of cards of 52, find the chance of a) no court cards (J, Q, K, A) b) at least one ace but no other court court cards c) at most one kind of court card
最佳解答:
a) P(no court card)=C(52-16,15)/C(52,15)=0.0124245 (6 sig fig) b) P(at least one ace but no other court cards) =[C(4,1)C(36,14)+C(4,2)C(36,13)+C(4,3)C(36,12)+C(4,4)C(36,11)]/C(52,15) =0.00773365 (6 sig fig) c) P(at most one kind of court card) =P(no court card)+P(exactly one court card) =0.0124245+C(5,1)C(4,1)C(36,14)/C(52,15) =0.0124245+0.0169425 =0.0293670 (6 sig fig)
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