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. = 0.7, p (a beats

c. = 0.9, p (b beats

c. = 0.3, 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?.189 correct: your answer is correct. (b) what is the probability that a wins both her matches?.63 correct: your answer is correct. (c) what is the probability that a loses both her matches?.03 correct: your answer is correct. (d) what is the probability that each person wins one match? (hint: there are two different ways for this to happen.).588 incorrect: your answer is incorrect.

Question

Sheldon Graham

Mathematics

14 September, 17:56

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. = 0.7, p (a beats

c. = 0.9, p (b beats

c. = 0.3, 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?.189 correct: your answer is correct. (b) what is the probability that a wins both her matches?.63 correct: your answer is correct. (c) what is the probability that a loses both her matches?.03 correct: your answer is correct. (d) what is the probability that each person wins one match? (hint: there are two different ways for this to happen.).588 incorrect: your answer is incorrect.

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Answers (1)

Know the Answer?

Leticia Coleman · Answer 1

A) P (A beats b) = 0.7 P (A beats C) = 0.9 Also P (b beats c) = 0.3

P (A wins both of her matches and b defeats c) = 0.7 * 0.9 * 0.3 = 0.189

B) P (A wins both of her matches) = 0.7 * 0.9 = 0.63

C) P (A loses against b) = 1 - 0.7 = 0.3 and against c = 1 - 0.9 = 0.1

P (A loses against b and c) = 0.1 * 0.3 = 0.03

D) Probability that A wins one match = (A beats B and B beats C and C beats A) + P (A beats C and C beats B and B beats A)

P = (A beats B) * P (B beats C) * P (C beats A) + P (A beats C) * P (C beats B) * P (B beats A) = (0.7) * (0.3) * (0.1) + (0.9) * (0.7) * (0.3) = 0.021 + 0.189 = 0.21