This season, the probability that the Yankees will win a game is 0.51 and the probability that the Yankees will score 5 or more runs in a game is 0.49 . The probability that the Yankees win and score 5 or more runs is 0.39 . What is the probability that the Yankees will lose when they score 5 or more runs? Round your answer to the nearest thousandth.
Answer
\( \boxed{0.204} \)
Step 1 ：Given probabilities: P(Yankees win) = 0.51, P(Yankees score 5 or more runs) = 0.49, P(Yankees win and score 5 or more runs) = 0.39
Step 2 ：Calculate P(Yankees lose and score 5 or more runs) = P(Yankees score 5 or more runs) - P(Yankees win and score 5 or more runs) = 0.49 - 0.39 = 0.1
Step 3 ：Use conditional probability formula: P(Yankees lose | Yankees score 5 or more runs) = P(Yankees lose and score 5 or more runs) / P(Yankees score 5 or more runs) = 0.1 / 0.49
Step 4 ：\( P(Yankees lose | Yankees score 5 or more runs) \approx 0.204 \)
Step 5 ：\( \boxed{0.204} \)
