Question

This season, the probability that the Yankees will win a game is 0.53 and the probability that the Yankees will score 5 or more runs in a game is 0.6. The probability that the Yankees lose and score fewer than 5 runs is 0.34. 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

We have P(lose) = 1 − 0.53 = 0.47. Since P(lose and score <5) = 0.34, then P(lose and score ≥5) = 0.47 − 0.34 = 0.13. Thus

P(score ≥5 | lose) = 0.13 / 0.47 ≈ 0.276596 ≈ 0.277 (to the nearest thousandth).