Question

This season, the probability that the Yankees will win a game is 0.59 and the probability that the Yankees will score 5 or more runs in a game is 0.43. The probability that the Yankees win and score 5 or more runs is 0.35. 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

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

P(win and score < 5) = P(win) − P(win and score ≥ 5) = 0.59 − 0.35 = 0.24.

So P(score < 5 | win) = 0.24 / 0.59 ≈ 0.407 (rounded to the nearest thousandth).