Question

An airline has 83% of its flights depart on schedule. It has 68% 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.
(Please help, I've been stuck on this one for half an hour!)

Answer 1

This question seems poorly-worded to me. Is it saying that it has a 68% chance of arriving on schedule whether or not it leaves on schedule?

Answer 2

Is this the exact wording of the question?

Answer 3

Sorry, it says "68% of its flights depart and arrive on schedule."

Answer 4

Still poorly-worded. It is either a case in which the 68% is the probability that it arrives on schedule given that it leaves on schedule, in which case finding the odds that it both leaves and arrives on schedule is the product of those to probabilities.

However to me it sounds like they are saying that 68% is the probability that it both leaves and arrives on schedule, in which case the odds that it both leaves and arrives on schedule is 68% and it's a sort of trick question.

I am inclined to think the first interpretation is right, but the wording is annoying.

Answer 5

I know, it's the exact wording though. But yes, the 68% both arrive and leave on schedule. Here's my answer choices:
0.56
0.81
0.82
0.15

Answer 6

well since 68% is not a choice, it is not a trick question
that would mean that 68% is the prob. that the plane arrives on time *given* that it left on time, so we can make the following diagram

Answer 7

But I'm not exactly sure how to get the probability of planes that both depart and arrive on time, when it says the percentage. I'm so confused!

Answer 8

or tabled ...