Question

question
this season, the probability that the yankees will win a game is 0.53 and the probability that the yankees will score 5 or more runs in a game is 0.62. the probability that the yankees win and score 5 or more runs is 0.41. 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 attempt 1 out of 2

Explanation:

Step1: Define events

Let \( W = \text{Yankees win} \), \( S \geq 5 = \text{score ≥5 runs} \). Given \( P(W)=0.53 \), \( P(S≥5)=0.62 \), \( P(W \cap S≥5)=0.41 \).

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

Use \( P(S<5 | W) = 1 - P(S≥5 | W) \). First find \( P(S≥5 | W) = \frac{P(W \cap S≥5)}{P(W)} = \frac{0.41}{0.53} \approx 0.77358 \).

Step3: Compute final probability

\( 1 - 0.77358 \approx 0.226 \). Rounded to nearest thousandth.

Answer:

0.226