Three basketball players compete in a basketball foul shooting contest. The eligible players are allowed one foul shot per round. After each round, all players who miss their foul shots are eliminated, and the remaining players participate in the next round. The contest ends when a single player who has not missed a foul shot remains, and is declared the winner, or when all players have been eliminated, and no one wins. In the past, player A has made an average of 80% of his foul shots, player B has made an average of 75%, and player C has made an average of 70%.

This contest can be modeled as an absorbing multichain by choosing as states all sets of players who have not been eliminated. For example, if two players remain, the corresponding states are the three pairs (A, B), (A, C), and (B, C). 

(a) Construct the transition probability matrix.

(b) What is the probability that the contest will end without a winner?

(c) What is the probability that player A will win the contest?

(d) If players B and C are the remaining contestants, what is the expected number of rounds needed before C wins?