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 not rain and the flight will leave on time is 0.81. What is the probability that the flight would be delayed when it is not raining? Round your answer to the nearest thousandth
To find the probability that the flight would be delayed when it is not raining, we can use the formula for conditional probability:
P(delayed | not raining) = P(delayed and not raining) / P(not raining)
We are given that:
P(rain) = 0.08
P(delayed) = 0.13
P(not rain and on time) = 0.81
From this information, we can calculate P(not raining) as:
P(not raining) = 1 - P(rain) = 1 - 0.08 = 0.92
Now, we can calculate P(delayed and not raining) using the formula:
P(delayed and not raining) = P(delayed) - P(delayed and raining)
P(delayed and not raining) = P(delayed) - P(rain)*P(delayed) = 0.13 - 0.08*0.13 = 0.1184
Finally, we can calculate P(delayed | not raining) using:
P(delayed | not raining) = P(delayed and not raining) / P(not raining)
P(delayed | not raining) = 0.1184 / 0.92 ≈ 0.129
Therefore, the probability that the flight would be delayed when it is not raining is approximately 0.129 (rounded to three decimal places).