This Demonstration simulates the behavior of an urn system under rules developed by G. Pólya. We start with some red and black balls in an urn. At each step we choose one randomly, replace it, and add

balls of the same color and

balls of the opposite color, where

and

are parameters. A special case is sampling without replacement, where

and

. In another special case, where

and

, the number of times that a red ball is chosen follows the

binomial distribution. The number of draws can range up to 1000, but the urn can be shown only if there are 200 or fewer draws.