The Cunning Space Traveller

An old space traveller is trying to trick the children of planet Naboo with an old trick. He has a hat full of a fixed number of black(B) and white(W) balls. He then asks one of the younglings to pick up a pair of balls from the hat at random. If they are of the same color, he asks the youngling to place a new white ball back into the hat, otherwise a new black ball is placed into the hat. This c