Two individuals, A and B, are finalists for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw. Suppose that the outcomes of successive games are independent, with P(A wins game) = .3, P(B wins game) = .2, and P(draw) = .5. Each time a player wins a game, he earns 1 point and his opponent earns no points. The first player to win 5 points wins the championship.
a. What is the probability that A wins the championship in just five games?
b. What is the probability that it takes just five games to obtain a champion?
c. If a draw earns a half-point for each player, describe how you would perform a simulation to estimate P(A wins the championship). Assume that the championship will end in a draw if both players obtain 5 points at the same time.