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Three friends (A, B, and C) will participate in a round-robin tournament in which each one...

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) = 0.8 P(A beats C) = 0.4 P(B beats C) = 0.6 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.

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