Question

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) = 0.3, P(A beats C) = 0.6, P(B beats C) = 0.2,

and that the outcomes of the three matches are independent of one another.

What is the probability that C will be the winner of the tournament?

Answer 1

The probability that C will be the winner of the tournament is 0.81.

Step-by-step explanation:

To find the probability that C will be the winner of the tournament, we need to consider all possible outcomes of the matches involving A, B, and C. Since each match outcome is independent, we can multiply the probabilities.

P(A beats B) = 0.3, P(A beats C) = 0.6, and P(B beats C) = 0.2.

The probability that C wins all its matches is P(A beats C) * P(B beats C) = 0.6 * 0.2 = 0.12.

However, C can also win if it loses to A but beats B, or if it loses to B but beats A. The probabilities for these cases are P(A beats C) * P(C beats B) = 0.6 * 0.8 = 0.48 and P(B beats A) * P(C beats A) = 0.7 * 0.3 = 0.21, respectively.

The total probability that C will be the winner of the tournament is the sum of these probabilities: 0.12 + 0.48 + 0.21 = 0.81.