Suppose that there are 6 balls in an urn, 2 red and 4 white. There are two players. The first player draws a ball at random. If the ball is white then it is replaced and the other player draws, and so forth, continuing until a red ball is drawn. The player drawing the first red ball loses.
a) What is the probability that the player who goes first wins? b) What is the probability that the player who goes first wins if after each draw of a white ball it is replaced in the urn by a red ball?