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) = 0.4 p(a beats c) = 0.3 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? (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.)