There are $b$ balls in an urn, exactly one of which is black. You choose $n$ balls from the urn at a time and throw away all non-black balls. If the black ball is chosen, it is replaced back into the urn. What is the expected number of times you pick the black ball, assuming you continue this process until all non-black balls are exhausted?
My thought was to use indicator variables; i.e. for pick number $i$, let $X_i = 1$ if the black ball was chosen, with $X_i = 0$ otherwise. Then $Y$, a random variable representing the number of times you pick the black ball, is given by $$Y = X_1 + X_2 + \cdots$$ but I'm not sure how to compute $E(Y)$.