I think I will continue posting some good questions from
Fridays Killer Questions 7city Learning:

Question:

There was a hit-and-run incident involving a taxi in a city in which 85% of the taxis
are green and the remaining 15% are blue. There was a witness to the crime who
says that the hit-and-run taxi was blue. Unfortunately this witness is only correct
80% of the time. What is the probability that it was indeed a blue car that hit our victim?

Answer:

Suppose that we have 100 such incidents. In 85 of these the taxi will have been
green and 15 blue, just based on random selection of taxi colour. In the cases where
the taxi was green the witness will mistakenly say that the car is blue 20% of the
time, i.e. 7 times. In the 15 blue cases the witness will correctly say blue 80% of the
time, i.e. 12 times. So although there were only 15 accidents involving a blue taxi
there were 29 reports of a blue taxi being to blame, and most of those (17 out of 29)
were in error. Now given that we were told it was a blue taxi, what is the probability
that it was a blue taxi? That’s just 12/29 or 41.4%.