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) = .7
P(A beats C) = .8
P(B beats C) = .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?