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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) = 0.5
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.)

Sagot :

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Answer:

0.27 ; 0.30 ; 0.20 ; 0.21

Step-by-step explanation:

Given that :

P(A beats B) = 0.5

P(A beats C) = 0.6

P(B beats C) = 0.9

Since the outcomes are independent :

A.) probability that A wins both her matches and that B beats C

P(A beats B) * P(A beats C) * P(B beats C)

0.5 * 0.6 * 0.9 = 0.27

B.) probability that A wins both her matches

P(A beats B) * P(A beats C)

0.5 * 0.6 = 0.3

C.) probability that A loses both her matches?

(1 - P(A beats B)) * (1 - P(A beats C)

(1 - 0.5) * (1 - 0.6)

0.5 * 0.4 = 0.20

D.) probability that each person wins one match

Either (A beats B), (B beats C). (C beats A) OR (A beats C), (C beats B), (B beats A)

Hence;

(0.5 * 0.9 * (1 - 0.6)) + (0.6 * (1 - 0.9) * (1 - 0.5)) = 0.21

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