Three friends (A, B, and C) will participate in a round-robin tournament in whic
ID: 2909714 • Letter: T
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) 0.8 P(A beats C)-0.9 P(B beats C)-0.5 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) Pr(A win both his matches and B beats C) = 0.8 * 0.9 * 0.5 = 0.36
(b) Pr(A wins both her matches) = 0.8 * 0.9 = 0.72
(c) Pr(A losses both her matches) = (1 - 0.8) * ( 1 - 0.9) = 0.02
(d) Pr(Each person win one match) = Pr(A wins B, B wins C and C wins A) + Pr(B wins A, A wins C and C wins B)
= 0.8 * 0.5 * (1 - 0.9) + (1 - 0.8) * 0.5 * 0.9
= 0.13