FRIDAY'S KILLER QUESTION: There was a hit and run incident involving a taxi...
Every Friday we'll be posting challenging and cryptic questions for you to answer, provided for us by 7city Learning. Post your answers in the comments box at the bottom of the page. Maximum kudos will be provided to the person who provides the correct answer first.
We'll add the correct answer to the bottom of this article on Monday morning.
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. These are the so-called positive one gets in medical tests.
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%.
