At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.16 and the probability that the flight will be delayed is 0.05. The probability that it will not rain and the flight will leave on time is 0.81. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.

Question

Mathematics

Raquel Hicks

16 April, 03:56

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.16 and the probability that the flight will be delayed is 0.05. The probability that it will not rain and the flight will leave on time is 0.81. 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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Answers (1)

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Erica Daugherty · Answer 1

0.853

Step-by-step explanation:

Use conditional probability. The probability of event A, given that event B has occurred, is:

P (A|B) = P (A and B) / P (B)

The probability that it is not raining, given that the flight leaves on time, is:

P (not raining | on time) = P (not raining AND on time) / P (on time)

P (not raining | on time) = 0.81 / (1 - 0.05)

P (not raining | on time) = 0.853