Seededplayers atashuffleboard tournament. Shuffleboard is an outdoor game popular with senior citizens. In singleelimination 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?
Outcome | Probability |
A defeats B | .9 |
A defeats C | .7 |
A defeats D | .6 |
B defeats C | .1 |
B defeats D | .2 |
C defeats D | .4 |
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