Three friends (A, B, and C) will participate in a round-robin tournament in whic

Question

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) = 0.2, P(A beats C) = 0.3, P(B beats C) = 0.8, 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 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.)

Explanation / Answer

a)

P(A beat B , A beats C , B beats C) = 0.2*0.3*0.8 = 0.048

b)

P(A beat B , A beats C) = 0.2*0.3 = 0.06

c)

P(B beats A , C beats A) = 0.8*0.7 = 0.56

d)

answered already

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