Players 1, 2, 3 are playing a tournament. Two of these three players are randomly chosen to play a game in round one, with the winner then playing the remaining player in round two. The winner of round two is the tournament victor. Assume that all games are independent and that i wins when playing against j with probability is i/( i+j)

(a) Find the probability that 1 is the tournament victor. (Hint: A tree diagram should be helpful, considering whether player 1 plays in round one.)

(b) If 1 is the tournament victor, find the conditional probability that 1 did not play in round one.