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?

Before the got the eyewitness report, the police were 85% certain that the taxi was blue. After an eyewitness confirmed that it was blue, their certainty dropped to 80%, since the distribution of taxis was no longer relevant, only the reliability of eyewitnesses.

On the other hand, should another, independant witness also confirm it was blue, the certainty will again change. At that point, the police will be only 64% certain that it was blue, but 96% sure (but not certain) that it wasn't green.

Posted by TomM on 2002-05-24 05:18:48