Three friends (A, B, and C) will participate in a round-robin tournament in whic
ID: 3179811 • Letter: T
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) = 0.4
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? (Hint: There are two different ways for this to happen.)
Explanation / Answer
Solution:
P(A beats B) = 0.4
P(A beats C) = 0.6
P(B beats C) = 0.9
a) P(A beats B , A beats C , B beats C) = 0.4 * 0.6 * 0.9 = 0.216
b) P(A beats B , A beats C) = 0.4 * 0.6 = 0.24
c) P(B beats A , C beats A) = 0.6*0.4 = 0.24
d) P(A beats B and B beats C and C beats A) + P(A beats C and C beats B and B beats A)
= P(A beats B)*P(B beats C)*P(C beats A)+ P(A beats C)*P(C beats B)* P(B beats A)
= 0.4*0.9*0.4 + 0.6*0.1*0.6 = 0.18