This season, the probability that the Yankees will win a game is 0.61 and the probability that the Yankees will score 5 or more runs in a game is 0.43 . The probability that the Yankees win and score 5 or more runs is 0.36 . What is the probability that the Yankees will lose when they score fewer than 5 runs? Round your answer to the nearest thousandth. Answer:

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Denote Events: Let's denote the events as follows: W: The Yankees win a game. S: The Yankees score 5 or more runs in a game. We are given the following probabilities: P(W) = 0.61 P(S) = 0.43 P(W and S) = 0.36  We want to find the probability that the Yankees lose and score fewer than 5 runs. Let's denote this event as L (Yankees lose) and F (Yankees score fewer than 5 runs). 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)Calculate Probability of Losing: Now, let's calculate the probability that the Yankees lose a game: P(L) = 1 - P(W) P(L) = 1 - 0.61 P(L) = 0.39Calculate Probability of Scoring Fewer Runs: Next, we need to find the probability that the Yankees score fewer than 5 runs. This is the complement of the probability that they score 5 or more runs. We can calculate this using the formula: P(F) = 1 - P(S)Calculate Probability of Losing and Scoring Fewer Runs: Now, let's calculate the probability that the Yankees score fewer than 5 runs: P(F) = 1 - P(S) P(F) = 1 - 0.43 P(F) = 0.57Round Final Answer: To find the probability that the Yankees lose and score fewer than 5 runs, we need to use the Multiplication Rule of Probability for independent events. However, we must first ensure that the events L and F are independent. Since we are not given any information about their dependence, we will assume they are independent for this calculation. The formula is: P(L and F) = P(L) * P(F)Now, let's calculate the probability that the Yankees lose and score fewer than 5 runs: P(L and F) = P(L) * P(F) P(L and F) = 0.39 * 0.57 P(L and F) = 0.2223Finally, we round the answer to the nearest thousandth as requested: P(L and F) ≈ 0.222

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