Question

This season, the probability that the Yankees will win a game is 0.6 and the probability that the Yankees will score 5 or more runs in a game is 0.44. The probability that the Yankees lose and score fewer than 5 runs is 0.32. What is the probability that the Yankees would score fewer than 5 runs when they lose the game? Round your answer to the nearest thousandth.

Answer 1

We want P(score < 5 | lose) = P(lose and score < 5) / P(lose).
P(lose) = 1 − P(win) = 1 − 0.6 = 0.4.
Thus the conditional probability = 0.32 / 0.4 = 0.8.

Rounded to the nearest thousandth: 0.800.