Problem

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 0.18 . 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 leave on time when it is not raining? Round your answer to the nearest thousandth.

Solution

Step 1 :Given probabilities: P(Rain) = 0.16, P(Delay) = 0.18, P(Not Rain and On Time) = 0.81

Step 2 :Find P(Not Rain): P(Not Rain) = 1 - P(Rain) = 1 - 0.16 = 0.84

Step 3 :Use conditional probability formula: P(On Time | Not Rain) = \(\frac{P(On Time and Not Rain)}{P(Not Rain)}\)

Step 4 :Calculate P(On Time | Not Rain): \(\frac{0.81}{0.84}\) = 0.964

Step 5 :\(\boxed{0.964}\) is the probability that the flight would leave on time when it is not raining.

From Solvely APP
Source: https://solvelyapp.com/problems/13148/

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