In a tournament involving players 1, 2, 3, 4, players 1 and 2 play a game, with the loser departing and the winner then playing against player 3, with the loser of that game departing and the winner than playing player 4. The winner of the game involving player 4 is the tournament winner. Suppose that a game between players i and j is won by player i with probability \frac{i}{i+j}.

(a) Find the expected number of games played by player 1.

(b) Find the expected number of games played by player 3.