Your job is to pick one ball from a collection of balls in such a way that every ball has an equal probability of being selected. The twist is that you do not know how many balls are in the collection. Each ball will be handed to you, one at a time. As each ball is handed to you you must decide (by some random process) whether to keep or discard the ball.

You must always be holding one and only one ball so that when a new ball is given to you, you must either discard it or keep it by discarding the previously held ball.