We need to pick a set of unique numbers (with replacement!) out of a collection of n unique numbers. Each number has the same probability to be picked. Each iteration we pick randomly one number from this collection. We end once we have a set of unique numbers where the amount of numbers in the set is exactly 10% of the original collection (amount of numbers in the set is n/10). What would be the mean of the amount of iterations we have to preform in order to get to this request?
Because we are allowed to keep choosing random numbers from the collection we are certain that eventually we will have a unique set, where the minimum amount of iterations are of course n/10, but what would be the mean amount of iterations??
I was trying to use Bernoulli method but quickly found out it is not covering the right answer. Is there something I am missing out? What would be the proper approach? Thanks for the Help