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) = 0.5
P(B beats C) = 0.3

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?

(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)

Explanation / Answer

a) probability that A wins both her matches and that B beats C = 0.2*0.5+0.3 = 0.40

b) probability that A wins both her matches = 0.2*0.5 = 0.10

c) each person winning one match can happen in 2 ways

i) A beats B, B beats C, C beats A
probability = 0.2*0.3*0.5 = 0.03

ii) B beats A, C beats B, A beats C
probability = (1-0.2)*(1-0.3)*0.5 = 0.28

thus required probability = 0.03 + 0.28 = 0.31

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