Three friends (A, B, and C) will participate in a round-robin tournament in whic

Question

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) = 0.6 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?

Explanation / Answer

Answer to the questions below:

a. P( A wins both & B beats C) = P( A wins against B)*P(A wins against C)*P( B beats C) = .8*.6*.9 = .432

b. P( A wins both her matches) = P( A wins against B)*P(A wins against C) = .8*.6 = .48

c. P( A looses both her matches) = (1-P(A beats B))*(1-P(A beats C)) = .2*.4 = .08

d. P(Each persons wins 1 match each ) = P( a beats b)*p( c beats a)*P( b beats c)+ P(b beats a)*P(a beats c)*P(c beats b)= .8*.4*.9 + .2*.6*.1 = .30

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