davido (04/01/83)
In-Real-Life: David H. Olson @ Tektronix, Instrument Division ---------- Suppose I've got an infinite collection of balls of which there are n different types. I will randomly choose balls hoping to eventually acquire all n distinct types. I know that the probability of getting the n different types after exactly n draws is n!/n^n. Also, the probability of getting k different types, k < n, after exactly k draws is n!/(n-k)! --------- . n^k However there are two problems which seem to be similar and have me stuck. What I want to do is better my chances of getting in the first case all n distinct balls, and in the second case k distinct balls, so I will continue to draw balls. For the first case, I'll draw t total balls, where t>n, and in the second case I'll draw t total balls where k < t < n. What are the probabilities of success for these two cases? For my particular application, typical numbers are n=100, k=50 and I need to find t such that there is a 90% probability of success, so enumeration (even by computer) is out.