A crime has occured in Carborough, involving a taxi. The police interviewed an eyewitness, who stated that the taxi involved was blue.

The police know that 85% of taxis in Carborough are blue, the other 15% being green. They also know that statistically witnesses in these situations tend to be correct 80% of the time - which means they report things wrong the other 20% of the time.

What is the probability that the taxi involved in the crime was actually blue?

Jim, I think you probably have the answer levik had in mind. Sometimes these exercises in pure probability run counter to apparent common sense. Sometimes even knowing that, it's hard to find the proper angle.

Levik, I couldn't think of how to phrase what I meant, but I think I've got it now (even though I now conceed that my approach was wrong, I don't want to leave you hanging.) When I said that the police would be 96% sure (but not certain) that it wasn't green, I was trying to state that there would be only a4% chance that it was green. And being 64% sure it was blue, would leave the other 32% where they had no way of determining whether it was blue or green.

Posted by TomM on 2002-05-25 04:15:37