Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) = 0.4 P(A beats C) = 0.8 P(B beats C) = 0.2 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? 0.064 (b) What is the probability that A wins both her matches? 0.32 (c) What is the probability that A loses both her matches? 0.12 (d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.) 0.07

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Chapter1: Combinatorial Analysis
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Need help with question D. Thanks in advance!

Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that
P(A beats B)
= 0.4
P(A beats C) = 0.8
P(B beats C) = 0.2
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?
0.064
(b) What is the probability that A wins both her matches?
0.32
(c) What is the probability that A loses both her matches?
0.12
(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
0.07
Transcribed Image Text:Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) = 0.4 P(A beats C) = 0.8 P(B beats C) = 0.2 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? 0.064 (b) What is the probability that A wins both her matches? 0.32 (c) What is the probability that A loses both her matches? 0.12 (d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.) 0.07
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