A Cab Company Was Involved in a Hit and Run

Short Answer

A cab company was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. 85% of the cabs in the city are green, while 15% are blue. A witness identified the cab as Blue. The court tested the reliability of the witness under the circumstances that existed on that night or the accident. The witness correctly identified the true colour 80% of the time, and failed 20% of the time. What is the prior probability that the cab involved in the accident is actually Blue? Following the test administered to the eyewitness, what is the posterior probability that the cab involved in the accident is actually Blue?