I am not much of a statistician and I have racked my brains around this problem without success: There are w white balls and b black balls in an urn. I want to get the distribution of the random variable S, the number of white balls obtained after n draws. The tricky part is, when a black ball is drawn, it is replaced in the urn, but when a white ball is drawn it is not replaced.
I have tried to start from the demonstrations of the binomial and hypergeometric distributions, but I get a huge expression that I can't simplify and that is increasingly complex as you increase the number of draws n.
It seems to be a rather simple problem but I couldn't find a solution on the internet. Is there a solution to this problem?
Thank you very much!