An airline has81% of its flights depart on schedule. It has 69% of its flights depart and arrive on schedule. Find the probability that a flight that departs on schedule also arrives on schedule. Round the answer to two decimal places.

Answer 1

Let A be the event that a flight departs on schedule and B be the event that a flight arrives on schedule. We want to find P(B|A), the probability that a flight arrives on schedule given that it departs on schedule. Using Bayes' theorem:

P(B|A) = P(A|B)P(B)/P(A)

We know P(A) = 0.81, the probability that a flight departs on schedule. We also know P(B) = 0.69, the probability that a flight departs and arrives on schedule. To find P(A|B), the probability that a flight departs on schedule given that it arrives on schedule, we can rearrange the formula:

P(A|B) = P(B|A)P(A)/P(B)

We can solve for P(A|B) by plugging in the values we know:

P(A|B) = P(B|A)P(A)/P(B)
0.81 = P(B|A) * 0.81 / 0.69
P(B|A) = 0.9444

So the probability that a flight that departs on schedule also arrives on schedule is 0.94, rounded to two decimal places.