Question

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.18 and the probability that the flight will be delayed is 0.13. 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 leave on time when it is raining? Round your answer to the nearest thousandth.

Answer 1

Let R = rain, O = on time, D = delayed. We have
P(R) = 0.18, P(D) = 0.13, P(not R and O) = 0.80.

P(not R) = 1 − 0.18 = 0.82, so P(not R and D) = 0.82 − 0.80 = 0.02.
Then P(R and D) = P(D) − P(not R and D) = 0.13 − 0.02 = 0.11.
Hence P(R and O) = P(R) − P(R and D) = 0.18 − 0.11 = 0.07.

Therefore P(O | R) = P(R and O)/P(R) = 0.07/0.18 ≈ 0.389.

Rounded to the nearest thousandth: 0.389.