## The taxi problem

Submitted by plusadmin on May 1, 1997May 1997

A witness sees a crime involving a taxi in Carborough. The witness says that the taxi is blue. It is known from previous research that witnesses are correct 80% of the time when making such statements. The police also know that 85% of the taxis in Carborough are blue, the other 15% being green. What is the probability that a blue taxi was involved in the crime?

### Solution

Thanks to *Steve Kallenborn* from Switzerland for correcting the originally published version of this problem.