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 0.52. the probability that the yankees win and score 5 or more runs is 0.43. 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.

Explanation:

Step1: Define events

Let \( W = \) Yankees win, \( S \geq 5 = \) score ≥5 runs, \( S < 5 = \) score <5 runs. Given \( P(W)=0.6 \), \( P(W \cap S \geq 5)=0.43 \).

Step2: Calculate \( P(S <5 | W) \)

Use \( P(S <5 | W) = 1 - P(S \geq5 | W) = 1 - \frac{P(W \cap S \geq5)}{P(W)} \)

Step3: Substitute values

\( 1 - \frac{0.43}{0.6} = 1 - 0.7167 \approx 0.283 \)

Answer:

0.283