Three friends (A, B, and C) will participate in a round-robin tournament in whic
ID: 3058857 • 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) = 0.7
P(A beats C) = 0.2
P(B beats C) = 0.9
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
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) = 0.7
P(A beats C) = 0.2
P(B beats C) = 0.9
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.)