Question

This season, the probability that the Yankees will win a game is 0.51 and the probability that the Yankees will score 5 or more runs in a game is 0.54. The probability that the Yankees lose and score fewer than 5 runs is 0.39. What is the probability that the Yankees will win when they score fewer than 5 runs? Round your answer to the nearest thousandth.

Answer 1

Let S^c be "score fewer than 5 runs." Then P(S^c)=1−0.54=0.46 and
P(W and S^c)=P(S^c)−P(L and S^c)=0.46−0.39=0.07.
So P(W | S^c)=0.07/0.46 ≈ 0.152.

Answer: 0.152.