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) 5 .2, and P(draw) = .5. Each time a player wins a game, he earns one point and his opponent earns no points. The first player to win five points wins the championship. For the sake of simplicity, assume that the championship will end in a draw if both players obtain five points at the same time.
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 experiment to estimate P(A wins the championship).
d. If neither player earns any points from a draw, would the simulation requested in Part (c) take longer to perform? Explain your reasoning.