By rewriting the formula for the multiplication rule you can

By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B|A)=P(A and B)/P(A)

Use the information below to find the probability that a flight departed on time given that it arrives on time.

The probability that an airplane flight departs on time is 0.89.

The probability that a flight arrives on time is 0.87.

The probability that a flight departs and arrives on time is 0.84.

Solution

Let A be the event that an airplane flight departs on time and B be the event that a flight arrives on time.

P(A and B ) = The probability that a flight departs and arrives on time = 0.84.

P(A) = The probability that an airplane flight departs on time is 0.89.

P(B|A)=P(A and B)/P(A) = 0.84/0.89 = 0.94