Question

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.19 and the probability that the flight will be delayed is 0.07. The probability that it will rain and the flight will be delayed is 0.02. What is the probability that the flight would be delayed when it is raining? Round your to the nearest thousandth

Answer 1

The probability that the flight will be delayed given that it is raining is calculated using the formula for conditional probability; the result is approximately 0.105.

Step-by-step explanation:

The question asks to find the probability that a flight will be delayed given that it is raining at LaGuardia Airport. To calculate this, we use the formula for conditional probability, which is the probability of the intersection of two events (in this case, rain and delay) divided by the probability of the event we are conditioning on (rain). Using the provided probabilities:

• Probability of rain (P(R)) = 0.19
• Probability of delay (P(D)) = 0.07
• Probability of both rain and delay (P(R and D)) = 0.02

The conditional probability of delay given rain is P(D|R) = P(R and D) / P(R) = 0.02 / 0.19. When you perform the division, you get approximately 0.105, and when rounded to the nearest thousandth, the result is 0.105.