at laguardia airport for a certain nightly flight, the probability that it will rain is 0.08 and the…

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 0.15. 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 answer to the nearest thousandth.

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 0.15. 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 answer to the nearest thousandth.

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Let $A$ be the event that the flight is delayed and $B$ be the event that it rains.

Step2: Identify the given probabilities

We are given that $P(B) = 0.08$ (probability of rain), $P(A)=0.15$ (probability of flight - delay), and $P(A\cap B)=0.02$ (probability of rain and flight - delay).

Step3: Calculate the conditional probability

Substitute the values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.02}{0.08}$. $P(A|B)=\frac{0.02}{0.08}=0.250$

Answer:

$0.250$