At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.19 and the probability that the flight will be delayed is 0.17 . The probability that it will rain and the flight will be delayed is 0.05 . 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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Events Denotation: 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) = 0.19 P(D) = 0.17 P(R and D) = 0.05  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 - 0.17 P(Not D) = 0.83Find 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 taking the complement of the probability of either raining or the flight being delayed. Using the Addition Rule of Probability, we have: P(R or D) = P(R) + P(D) - P(R and D) P(R or D) = 0.19 + 0.17 - 0.05 P(R or D) = 0.31  Now, we find the complement of P(R or D) to get P(Not R and Not D): P(Not R and Not D) = 1 - P(R or D) P(Not R and Not D) = 1 - 0.31 P(Not R and Not D) = 0.69Calculate Conditional Probability: Now we can use the definition of conditional probability to find P(Not R | Not D). The formula for conditional probability is: P(Not R | Not D) = P(Not R and Not D) / P(Not D)  Substituting the values we have found: P(Not R | Not D) = 0.69 / 0.83 P(Not R | Not D) ≈ 0.8313Final Probability Calculation: Finally, we round the answer to the nearest thousandth as requested: P(Not R | Not D) ≈ 0.831

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