Question

This season, the probability that the Yankees will win a game is 0.54 and the probability that the Yankees will score 5 or more runs in a game is 0.46. The probability that the Yankees lose and score fewer than 5 runs is 0.37. What is the probability that the Yankees win and score 5 or more runs? Round your answer to the nearest thousandth.

Answer 1

Let W = win, S = score ≥ 5. Then P(L) = 1 − 0.54 = 0.46. Given P(L ∩ S^c) = 0.37, so P(L ∩ S) = 0.46 − 0.37 = 0.09.
Since P(S) = P(W ∩ S) + P(L ∩ S), we have 0.46 = P(W ∩ S) + 0.09, so P(W ∩ S) = 0.37.

Answer: 0.370.