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.)

Question

Mathematics

Haylie

7 July, 14:44

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.)

+2

Answers (1)

Know the Answer?

Cohen · 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