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?

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Author:Amos Gilat
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**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.)
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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