6.54 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) 5 .7 P(A beats C) 5 .8 P(B beats C) 5 .6 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.)