Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose tha P(A beats B) = 0.6 P(A beats C) = 0.2 P(B beats C) = 0.4 and that the outcomes of the three matches are independent of one another. (a) What is the probability that A wins both her matches and that B beats C? (b) What is the probability that A wins both her matches? (c) What is the probability that A Joses both her matches?
Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose tha P(A beats B) = 0.6 P(A beats C) = 0.2 P(B beats C) = 0.4 and that the outcomes of the three matches are independent of one another. (a) What is the probability that A wins both her matches and that B beats C? (b) What is the probability that A wins both her matches? (c) What is the probability that A Joses both her matches?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Round-Robin Tournament Probability**
Three friends (A, B, and C) will participate in a round-robin tournament, where each player competes against the other two. Suppose the following probabilities:
- \( P(A \text{ beats } B) = 0.6 \)
- \( P(A \text{ beats } C) = 0.2 \)
- \( P(B \text{ beats } C) = 0.4 \)
The outcomes of the matches are independent of one another.
**Questions:**
(a) What is the probability that A wins both her matches and that B beats C?
(b) What is the probability that A wins both her matches?
(c) What is the probability that A loses both her matches?
(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
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