At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.09 and the probability that the flight will be delayed is 0.08 . The probability that it will rain and the flight will be delayed is 0.01 . What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth. Answer:

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Denote Events: Let's denote the events as follows: R: It will rain. D: The flight will be delayed. We are given the following probabilities: P(R) = 0.09 P(D) = 0.08 P(R and D) = 0.01  We want to find the probability that it is not raining given that the flight leaves on time. This can be expressed as P(Not R | Not D), which is the conditional probability of it not raining given that the flight is not delayed.Find Probability Not Delayed: First, we need to find the probability of the flight not being delayed, which is P(Not D). This is the complement of the flight being delayed, so we calculate it as: P(Not D) = 1 - P(D) P(Not D) = 1 - 0.08 P(Not D) = 0.92Find Probability Not Rain and Not Delayed: Next, we need to find the probability of it not raining and the flight not being delayed, which is P(Not R and Not D). This can be found by subtracting the probability of it raining and the flight being delayed from the probability of it raining, and then subtracting this result from the probability of the flight not being delayed: P(Not R and Not D) = P(Not D) - P(R and D) P(Not R and Not D) = 0.92 - 0.01 P(Not R and Not D) = 0.91Find Conditional Probability: Now we can find the conditional probability P(Not R | Not D) using the formula: P(Not R | Not D) = P(Not R and Not D) / P(Not D) Substituting the values we have: P(Not R | Not D) = 0.91 / 0.92 P(Not R | Not D) ≈ 0.9891Round Final Answer: Finally, we round the answer to the nearest thousandth as requested: P(Not R | Not D) ≈ 0.989

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