93 Seeded players at a shuffleboard tournament. Shuffleboard is an outdoor game popular with senior citizens. In single elimination shuffleboard tournaments, players are paired and play a match against each other, with the winners moving on to play another match. The tournament concludes in a final that matches two undefeated players. The winner of the final match is the overall tournament champion.

Chance (Winter 2006) investigated the probability of winning a shuffleboard tournament with 64 players. As an example, the authors considered a small tournament with only 4 players, named A , B , C , and D . This tournament involves a total of three matches. In the first round, A plays B in one match and C plays D in the other match.

Then the winners play in the final round.

a. List the different outcomes of the tournament. (For example, one outcome is “ A and C win first-round matches and A wins the final.”)

b. If the players are of equal ability, what is the probability that A wins the tournament?

c. Suppose the players are not of equal ability. The accompanying table gives the likelihood of one player defeating the other. ( Example: The probability that A defeats B is .9.) What is the probability that A wins the tournament?

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Outcome Probability A defeats B .9 A defeats C A defeats D B defeats C B defeats D C defeats D 76124 .7 .6 .2 .4