Possible Duplicate:
Expected number of draws until the first good element is chosen
An urn contains $b$ blue balls and $r$ red balls. Balls are removed at random without replacement until the first blue ball is drawn. What is the expectation of the total number of balls drawn? The answer should be $\frac{b+r+1}{b+1}$ but I have not been able to prove it.
I know that this seems like an easy/classic problem but I tried brute force (definition of expectation) and got a sum that I'm not able to simplify. Then I tried looking up well known distributions but none of them works for this problem.