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) = 0.6, 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.)