Please provide an explanation for part d. Three friends (A, B, and C) will parti

Question

Please provide an explanation for part d.

Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose th P(A beats B) = 0.8 P(A beats C)-0.6 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? 0.144 (b) What is the probability that A wins both her matches? 0.48 (c) What is the probability that A loses both her matches? 0.08 (d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)

Explanation / Answer

(d) There are two ways for each person to win one match

i. A beats B : In this case B beats C and C beats A

Probability = 0.8 * 0.3 * (1 - 0.6)

= 0.096

ii. A beats C: In this case C beats B and B beats A

Probability = 0.6 * (1 - 0.3) * (1 - 0.8)

= 0.084.

=> Probability that each player wins one game

= 0.096 + 0.084

= 0.18.

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