Answer:
Step-by-step explanation:
To find the probability that the Yankees would score fewer than 5 runs when they win the game, we can use conditional probability.
Let \( A \) be the event that the Yankees win a game, and let \( B \) be the event that the Yankees score 5 or more runs in a game.
We are given:
- \( P(A) = 0.59 \) (probability that the Yankees win a game)
- \( P(B) = 0.43 \) (probability that the Yankees score 5 or more runs in a game)
- \( P(A \cap B) = 0.35 \) (probability that the Yankees win and score 5 or more runs)
We can use the formula for conditional probability:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
This formula calculates the probability of event \( A \) occurring given that event \( B \) has already occurred.
So, substituting the given values:
\[ P(A|B) = \frac{0.35}{0.43} \]
\[ P(A|B) \approx 0.814 \]
So, the probability that the Yankees would score fewer than 5 runs when they win the game is approximately \( 1 - 0.814 = 0.186 \), rounded to the nearest thousandth.