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Homework Statement
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) = 0.7, P(A beats C) = 0.3, P(B beats C) = 0.6, 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.)
Homework Equations
not sure if there is a relevant equation to this
The Attempt at a Solution
(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
so A, B and C would need to win a match
P(A beats B) = 0.7 (A wins)
P(A beats C) = 0.3, so we would take 1-.3=0.7 to figure out probability of C winning
P(B beats C) = 0.6 (B wins)
P=(0.7)(0.7)(0.6)=0.294 THIS IS INCORRECT