Answered

Explore a wide range of topics and get answers from experts on IDNLearn.com. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.

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 :

Fichohidn

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

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.