The taxi problem revisited

In this issue's article "Image analysis - a modern application of mathematics", Julian Stander introduced the idea of using Bayes' Theorem to update our beliefs based on new information.

We can use Bayes' Theorem to solve the taxi problem in Issue No. 2 (see "The taxi problem" ):

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

Solution