Three friends (a, b, andc.will participate in a round-robin tournament in which each one plays both of the others. suppose that p(a beatsb.= 0.7, p(a beatsc.= 0.9, p(b beatsc.= 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
Answer:
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
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11 months ago
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