At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.13 and the probability that the flight will be delayed is 0.1. The probability that it will rain and the flight will be delayed is 0.05 . What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth. Answer:

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Events Denoted: Let's denote the events as follows: R: It will rain. D: The flight will be delayed. R': It will not rain (the complement of R). D': The flight will leave on time (the complement of D).  We are given the following probabilities: P(R) = 0.13 P(D) = 0.1 P(R and D) = 0.05  We want to find P(D' and R'), which is the probability that the flight leaves on time and it is not raining.  First, we need to find P(R'), which is the probability that it does not rain. This is the complement of P(R), so we calculate it as: P(R') = 1 - P(R) P(R') = 1 - 0.13 P(R') = 0.87Calculate Probabilities: Next, we need to find P(D), which is already given as 0.1. To find P(D'), we calculate the complement of P(D): P(D') = 1 - P(D) P(D') = 1 - 0.1 P(D') = 0.9Find P(D' and R'): Now, we need to find P(D' and R'), but we don't have this probability directly. We can use the fact that P(D' and R') is part of P(R'), and we can subtract the probability of the flight being delayed when it rains from P(R').  We know that P(R and D) is the probability that it will rain and the flight will be delayed. However, we need to find the probability that the flight will be delayed given that it is raining, which is P(D | R). We can use the definition of conditional probability: P(D | R) = P(R and D) / P(R) P(D | R) = 0.05 / 0.13 P(D | R) ≈ 0.385  Now, we can find P(D' | R), which is the probability that the flight leaves on time given that it is raining: P(D' | R) = 1 - P(D | R) P(D' | R) ≈ 1 - 0.385 P(D' | R) ≈ 0.615Correcting Previous Mistake: However, we made a mistake in the previous step. We don't need to find P(D' | R) because we are looking for P(D' and R'), which is the probability that the flight leaves on time and it is not raining. We need to correct this error and find P(D' and R') directly.  Since P(R and D) is the intersection of R and D, we can find the probability of the flight leaving on time when it is not raining by subtracting P(R and D) from P(R'):  P(D' and R') = P(R') - P(R and D) P(D' and R') = 0.87 - 0.05 P(D' and R') = 0.82

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