Question

This season, the probability that the Yankees will win a game is 0.61 and the probability that the Yankees will score 5 or more runs in a game is 0.62. The probability that the Yankees lose and score fewer than 5 runs is 0.31. What is the probability that the Yankees would score fewer than 5 runs when they win the game? Round your answer to the nearest thousandth.

Answer 1

P(score < 5 | win) = P(score < 5 and win) / P(win).

P(score < 5) = 1 − 0.62 = 0.38. Given P(lose and score < 5) = 0.31, so P(win and score < 5) = 0.38 − 0.31 = 0.07.

Thus P(score < 5 | win) = 0.07 / 0.61 ≈ 0.115.