This season, the probability that the Yankees will win a game is 0.54 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 will lose when they score 5 or more runs? Round your answer to the nearest thousandth. Answer:

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Events Denoted: Let's denote the events as follows: W: The Yankees win a game. R: The Yankees score 5 or more runs in a game. L: The Yankees lose a game.  We are given the following probabilities: P(W) = 0.54 P(R) = 0.52 P(W and R) = 0.43  We want to find the probability that the Yankees will lose when they score 5 or more runs, which can be denoted as P(L and R).Find Probability of Losing: First, we need to find the probability that the Yankees lose a game, which is the complement of the probability that they win. We can calculate this using the formula: P(L) = 1 - P(W) Substituting the given value for P(W), we get: P(L) = 1 - 0.54 P(L) = 0.46Find Probability of Losing and Scoring: Next, we need to find the probability that the Yankees lose and score 5 or more runs. We can use the formula for the conditional probability: P(L and R) = P(R) - P(W and R) Substituting the given values, we get: P(L and R) = 0.52 - 0.43 P(L and R) = 0.09Calculate Conditional Probability: Now, to find the probability that the Yankees will lose when they score 5 or more runs, we need to calculate the conditional probability P(L | R), which is the probability of L given R. We can use the formula: P(L | R) = P(L and R) / P(R) Substituting the values we have found, we get: P(L | R) = 0.09 / 0.52 P(L | R) ≈ 0.173Round Final Answer: Finally, we round the answer to the nearest thousandth as requested: P(L | R) ≈ 0.173 Rounded to the nearest thousandth, P(L | R) ≈ 0.173

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