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) = 0.3
P(B beats C) = 0.7
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.)

Answer 1

(a) P(A BEATS B) × P(A BEATS C) × P(B BEATS C)
= 0.4×0.3×0.7=0.084
(b) P(A BEATS B)×P(A BEATS C)=0.4×0.3=0.12
(c) P(B BEATS A)×P(C BEATS A)=0.6×0.7=0.42
(d) P(A BEATS B)×P(C BEATS A)×P(B BEATS C)
+ P(B BEATS A )×P(A BEATS C)×P(C BEATS B)
= 0.5×0.7×0.7+0.6×.0.3×0.3=.25