Two individuals, A and B, are finalists for a chess

Chapter 0, Problem 6.99

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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. For the sake of simplicity, assume that the championship will end in a draw if both players obtain 5 points at the same time.a. What is the probability that A wins the championship injust five games?b. What is the probability that it takes just five games toobtain a champion?c. If a draw earns a half-point for each player, describehow you would perform a simulation to estimate P(A winsthe championship).d. If neither player earns any points from a draw, wouldthe simulation in Part (c) take longer to perform? Explainyour reasoning