Get the answers you've been searching for with IDNLearn.com. Our community is ready to provide in-depth answers and practical solutions to any questions you may have.

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 :

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

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.