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 0.13. The probability that it will rain and the flight will be delayed is 0.06. What is the probability that the flight would be delayed when it is not raining? Round your answer to the nearest thousandth.

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
6 months ago

To find the probability that the flight will be delayed when it is not raining, we will use the formula for conditional probability:

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

Where:
- A: Flight is delayed
- B: It is not raining

We know that:
- P(A) = 0.13 (probability that the flight will be delayed)
- P(B) = 1 - P(rain) = 1 - 0.08 = 0.92 (probability that it is not raining)
- P(A and B) = 0.06 (probability that it will rain and the flight will be delayed)

Now we can plug these values into the formula:

P(A|B) = 0.06 / 0.92

P(A|B) ≈ 0.065

Therefore, the probability that the flight would be delayed when it is not raining is approximately 0.065 or 6.5%.