Three friends A B and C will participate in a roundrobin tou

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) = 0.5, P(B beats C) = 0.4, and that the outcomes of the three matches are independent of one another.

(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)

Solution

a) 0.8 * 0.5 * 0.4 = .16

b) 0.8 * 0.5 = 0.4

c) 0.5 * 0.8 = 0.4

d) This can happen two ways.
A beats B, B beats C, C beats A or
A beats C, C beats B, B beats A.

( 0.8 * 0.4 * 0.8 ) + ( 0.5 * 0.4 * 0.5 ) = 0.256 + .1 = .356