What is the Probability that Each Person Wins One Match?

[needstatshelp]

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

 

[tiny-tim]

hi needstatshelp! welcome to pf!

(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
…
P=(0.7)(0.7)(0.6)=0.294 THIS IS INCORRECT

you've only done the probability for one of the two different ways