In the problem of points discussed in the historical remarks in Section 3.2 two

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 thatN = 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.