At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.08 and the probability that the flight will be delayed is 0.15 . The probability that it will not rain and the flight will leave on time is 0.8 . What is the probability that the flight would be delayed when it is raining? 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. ¬R: It will not rain. ¬D: The flight will leave on time.  We are given the following probabilities: P(R) = 0.08 P(D) = 0.15 P(¬R and ¬D) = 0.8  We need to find the probability that the flight would be delayed when it is raining, which is P(D|R). First, we need to find P(R and D), the probability that it will rain and the flight will be delayed. We can use the Complement Rule and the Addition Rule of Probability to find this.  The Complement Rule states that P(A) = 1 - P(¬A), and the Addition Rule states that P(A or B) = P(A) + P(B) - P(A and B).  We can find P(R or D) by using the Complement Rule on P(¬R and ¬D): P(R or D) = 1 - P(¬R and ¬D) = 1 - 0.8 = 0.2Find P(R and D): Now, we can use the Addition Rule to find P(R and D): P(R and D) = P(R) + P(D) - P(R or D) = 0.08 + 0.15 - 0.2Find P(R and D): Let's calculate P(R and D): P(R and D) = 0.08 + 0.15 - 0.2 = 0.03Find P(D|R): Finally, we can find P(D|R), the probability that the flight will be delayed given that it is raining, by using the definition of conditional probability: P(D|R) = P(R and D) / P(R)Calculate P(D|R): Now we calculate P(D|R): P(D|R) = 0.03 / 0.08Calculate P(D|R): After performing the division, we get: P(D|R) = 0.375 However, we need to round the answer to the nearest thousandth as instructed.Rounded Probability: Rounded to the nearest thousandth, the probability is: P(D|R) ≈ 0.375 (No rounding needed as it is already at the thousandth place)

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