The Taxi-cab Problem

A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. 90% of the cabs in the city are Green and 10% are Blue.

A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.

What is the probability that the cab involved in the accident was Blue rather than Green knowing that this witness identified it as Blue?