Three friends (A, B, and C) will participate in a round-robin tournament in whic
ID: 3338396 • 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)0.5, P(B beats C)0.7, 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? .28 (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 ta each person wins one match? (HintThere are two different ways for this to happen.)Explanation / Answer
a) P(A wins both her matches and B beats C) = P(A beats B) * P(A beats C) * P(B beats C) = 0.8 * 0.5 * 0.7 = 0.28
b) P(A wins both her match) = P(A beats B) * P(A beats C) = 0.8 * 0.5 = 0.4
c) P(A looses both her matches) = P(B beats A) * P(C beats A) = (1 - 0.8) * (1 - 0.5) = 0.1
d) P(each person wins one match) = P(A beats B) * P(B beats C) * P(C beats A) + P(A beats C) * P(C beats B) * P(B beats A)
= 0.8 * 0.7 * (1 - 0.5) + 0.5 * (1 - 0.7) * (1 - 0.8)
= 0.31