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 succes- sive 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. For the sake of simplicity, assume that the championship will end in a draw if both play- ers obtain 5 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 to estimate P(A wins the championship).

d. If neither player earns any points from a draw, would the simulation in Part (c) take longer to per- form? Explain your reasoning.