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 0.57. The probability that the Yankees lose and score fewer than 5 runs is 0.31. What is the probability that the Yankees would score 5 or more runs when they lose the game? Round your answer to the nearest thousandth.

Answer 1

Let L = lose and S = score ≥5. Then P(L) = 1 − 0.61 = 0.39. Given P(L ∩ S^c) = 0.31, so P(L ∩ S) = 0.39 − 0.31 = 0.08. Thus

P(S | L) = 0.08 / 0.39 ≈ 0.205.

Rounded to the nearest thousandth: 0.205.