How many balls fall in a given bin?The number of balls that fall in a given bin follows the binomial distribution b(k; n, 1/b). If n balls are tossed, so the expected number of balls that fall in the given bin is n/b.
How many balls must one toss, on the average, until a given bin contains a ball?The number of tosses until the given bin receives a ball follows the geometric distribution with probability 1/b and, the expected number of tosses until success is 1/(1/b) = b.