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4 In the bottom of the ninth inning in a tie game the leadoff batter...

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4 In the bottom of the ninth inning in a tie game the leadoff batter for the home team hits a double According to researcher Tom Tango teams in this situation have a win probability of 0 807 Because the home team only needs 1 run to win the game some managers will choose to have the next player attempt a sacrifice bunt which allows the runner on second base to reach third base while the hitter is thrown out If the sacrifice bunt is successful then the home team has a runner on third base with 1 out and a win probability of 0 830 However if the sacrifice bunt is unsuccessful and the runner is thrown out at third the home team has a runner on first with 1 out and a win probability of 0 637 Assume that the hitter is able to bunt the ball and doesn t strike out walk etc a Interpret the value of 0 807 in the context of this problem b Create a tree diagram for a sacrifice bunt attempt using the possible outcomes of the attempt as the first set of branches and the possible outcomes of the game as the second set of branches Assume that the hitter has a 0 75 probability of successfully executing the sacrifice bunt

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