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 in just five games? b. What is the probability that it takes just five games to obtain a champion? c. Ifadrawearnsahalf-pointforeachplayer,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 perform? Explain your reasoning.
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
b. What is the probability that it takes just five games to obtain a champion?
c. Ifadrawearnsahalf-pointforeachplayer,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 perform? Explain your reasoning.
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