Question

This season, the probability that the Yankees will win a game is 0.47 and the probability that the Yankees will score 5 or more runs in a game is 0.56. The probability that the Yankees win and score 5 or more runs is 0.4. What is the probability that the Yankees lose and score fewer than 5 runs? Round your answer to the nearest thousandth.

Answer 1

Let W = win and S = score ≥ 5. We want P(W^c ∧ S^c) = 1 − P(W ∪ S) = 1 − [P(W) + P(S) − P(W ∧ S)].

So P = 1 − (0.47 + 0.56 − 0.40) = 1 − 0.63 = 0.37.

Rounded to the nearest thousandth: 0.370.