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?