I have a problem dealing with expected values. I'll jump right into the problem: There are 3 red and 1 black balls in an urn. What is the expected number of times a ball must be removed before a black ball is removed. I originally thought of this using E[X]=1*P(X=1) + 2*P(X=2) + ... I filled in P's using hyper geometric distribution. But didn't get the correct result. Trying a uniform for each trial I did this 1*1/4 + 2*1/3 + 3*1/2 + 4*1/1 I found the following as a solution from a LONG derivation of formulas: k(r+b+1)/(b+1) where k=1 in this case. From a problem setup the same but using negative hyper geometric. This makes no sense to me. Is there some more simple way of thinking of this?