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Sampling of one object at a time with replacement is being carried out from a batch of N objects. Assuming that the selection is at tandom, find the probability that all of the first M objects sampled(M<=N) are different.Deduce the probability that there is at least one repeat among the first M objects, and show that the probability that the first repeat occurs on the K^th drawing is (N-1)(K-1)/N^K-1(N-K+1)! for 2<=K<= N
ANSWER
The probability that all of the first M objects sampled(M<=N) are different
=1*(N-1)/N*(N-2)/N*...*(N-M+1)/N
=(N-1)!/[M!N^(M-1)]
The probability that there is at least one repeat among the first M objects
=1-(N-1)!/[M!N^(M-1)]
The probability that the first repeat occurs on the K^th drawing
=1*(N-1)/N*(N-2)/N*...*(N-K+2)/N*(K-1)/N*1*1*1*...*1
=(N-1)!(K-1)/[(N-K+1)!N^(K-1)]

2007-11-12 13:03:04 補充：
你最後提供的答案應該漏了!