Question

Kaden, Keith, and Kipp compete in a series of daily 3-way races. For each race, the probability that Kaden wins is 1/6, the probability that Keith wins is 1/2, and the probability that Kipp wins is 1/3. On a day that Kaden doesn't win, what is the probability that Keith beats Kipp?​

Answer 1

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Answer:

3/5

Explanation:

Let a, b, c represent the probability of a win by Kaden, Keith, and Kipp, respectively.

P(bc' | a') = P(a'bc')/P(a')

P(bc' | a') = (1/2)/(1 -1/6) = (3/6)/(5/6) = 3/5

The probability is 3/5 that Keith beats Kipp when Kaden doesn't win.