A discrete probability distribution that arises from the following model; Suppose an urn contains n balls of which one is red and the remainder are white. Sampling with replacement of a white ball (if drawn) by a red ball continues until a red ball is drawn. Then the probability distribution of the required number of draws, Y, is

                                                   Pr (y = y) = (n 1) !y / (n y) !n exp(y)

After n 1 draws the urn contains only red balls and so no more than n draws are required.