Problem

Seededplayers atashuffleboard tournament. Shuffleboard is an outdoor game popular with sen...

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

Step-by-Step Solution

Request Professional Solution

Request Solution!

We need at least 10 more requests to produce the solution.

0 / 10 have requested this problem solution

The more requests, the faster the answer.

Request! (Login Required)


All students who have requested the solution will be notified once they are available.
Add your Solution
Textbook Solutions and Answers Search