Create a tree diagram for an attempt to score on the play, using the possible outcomes or the attempt as the first set of branches and the possible outcomes of the game as the second set of branches. Use p for the probability of a successfully scoring on the play.

The 2014 World Series between Kansas City Royals and San Francisco Giants went to a winner-take-all Game 7. In the bottom of the ninth inning of Game 7, the Royals were trailing by 1 run and quickly made 2 outs. The next batter, Alex Gordon, hit a ball that was displayed by an outfielder, allowing Gordon to easily make it to third base. In fact, many people thought that Gordon could have made it all the way home to score the tying run. Should the third base coach have sent him? The win probability for a team with a runner on third base, down by 1 with 2 outs in the ninth inning is 0.170. If the runner goes for home and successfully ties the game, their win probability increases from 0.532. However, if the runner goes for home and is thrown out, their win probability decreases to 0.

Using the tree diagram for the attempt to score, express the probability of a win for the Royals in terms of p. (1-p)+(0.532p) 0.532p 0.468p 0 For what values of p would it be worthwhile to attempt to score on the play? p 0.532

p 0.320 p 0.170 p1