Question

This season, the probability that the Yankees will win a game is 0.58 and the probability that the Yankees will score 5 or more runs in a game is 0.55. The probability that the Yankees lose and score fewer than 5 runs is 0.3. 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 are given:
- P(win) = 0.58
- P(score ≥ 5) = 0.55 → P(score < 5) = 0.45
- P(lose and score < 5) = 0.30

Compute P(win and score < 5) = P(score < 5) − P(lose and score < 5) = 0.45 − 0.30 = 0.15.

Then P(score < 5 | win) = P(win and score < 5) / P(win) = 0.15 / 0.58 ≈ 0.259.

Rounded to the nearest thousandth: 0.259.