In the problem of points, discussed in the historical remarks in Section 3.2, two players, A and B, play a series of points in a game with player A winning each point with probability p and player B winning each point with probability q=1−p. The first player to win N points wins the game. Assume that N=3. Let X be a random variable that has the value 1 if player A wins the series and 0 otherwise. Let Y be a random variable with value the number of points played in a game. Find the distribution of X and Y when p=1/2. Are X and Y independent in this case? Answer the same questions for the case p=2/3.