If I spin the roulette (numbers from 0 to 36) N consecutive times, how many different numbers should I expect to get?

(If N=1, your formula should give 1 as an answer, but for N=2, it should be a little under 2, and for all other N, the formula should be less than the minimum of N and 37.)

Another question: how many times should you spin the roulette, so chances are better than one in a million, that all 37 numbers will have appeared?

When Dn denotes the different numbers on spinning the roulette n times, Dn is given by

Dn = 1 + 36*(Dn-1)/37

D1 = 1

However I would like to see Dn in terms of n rather than Dn-1 which leads to recursion.

Your help is needed to take it further...

Posted by Rupesh Khandelwal on 2005-04-16 10:22:59