Question This season, the probability that the Yankees will win a game is 0.48 and the probability that the Yankees will score 5 or more runs in a game is 0.6 . The probability that the Yankees win and score 5 or more runs is 0.38. What is the probability that the Yankees will win when they score fewer than 5 runs? Round your answer to the nearest thousandth. Answer Attemptiout of 2 square

To find the probability that the Yankees will win when they score fewer than 5 runs, we can use the formula for conditional probability:<br /><br />\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]<br /><br />where:<br />- \( A \) is the event that the Yankees win.<br />- \( B \) is the event that the Yankees score fewer than 5 runs.<br /><br />First, we need to determine \( P(B) \), the probability that the Yankees score fewer than 5 runs. We know that:<br /><br />\[ P(\text{Yankees score 5 or more runs}) = 0.6 \]<br /><br />Therefore, the probability that the Yankees score fewer than 5 runs is:<br /><br />\[ P(\text{Yankees score fewer than 5 runs}) = 1 - 0.6 = 0.4 \]<br /><br />Next, we need to find \( P(A \cap B) \), the probability that the Yankees win and score fewer than 5 runs. We know that:<br /><br />\[ P(\text{Yankees win and score 5 or more runs}) = 0.38 \]<br /><br />Therefore, the probability that the Yankees win and score fewer than 5 runs is:<br /><br />\[ P(\text{Yankees win and score fewer than 5 runs}) = P(\text{Yankees win}) - P(\text{Yankees win and score 5 or more runs}) \]<br /><br />Given that \( P(\text{Yankees win}) = 0.48 \):<br /><br />\[ P(\text{Yankees win and score fewer than 5 runs}) = 0.48 - 0.38 = 0.10 \]<br /><br />Now, we can use the conditional probability formula:<br /><br />\[ P(\text{Yankees win | score fewer than 5 runs}) = \frac{P(\text{Yankees win and score fewer than 5 runs})}{P(\text{Yankees score fewer than 5 runs})} \]<br /><br />\[ P(\text{Yankees win | score fewer than 5 runs}) = \frac{0.10}{0.4} = 0.25 \]<br /><br />Therefore, the probability that the Yankees will win when they score fewer than 5 runs is \( 0.250 \).