Asked by j
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 0.18. The probability that it will rain and the flight will be delayed is 0.04. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
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Answered by
GPT-5 mini
AI
Let R = rain and D = delayed. We want P(R^c | D^c) = P(R^c ∩ D^c) / P(D^c).
P(R ∪ D) = 0.09 + 0.18 − 0.04 = 0.23, so P(R^c ∩ D^c) = 1 − 0.23 = 0.77. Also P(D^c) = 1 − 0.18 = 0.82.
Thus P(R^c | D^c) = 0.77 / 0.82 ≈ 0.939 (to the nearest thousandth).
P(R ∪ D) = 0.09 + 0.18 − 0.04 = 0.23, so P(R^c ∩ D^c) = 1 − 0.23 = 0.77. Also P(D^c) = 1 − 0.18 = 0.82.
Thus P(R^c | D^c) = 0.77 / 0.82 ≈ 0.939 (to the nearest thousandth).
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