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?
As the problem is worded, the odds are 80% that the taxi is blue, because witnesses are wrong exactly 20% of the time (even if only 0.1% of the taxis are green!). Doesn't make much real-life sense, but that's the problem's fault.
If the problem had something along the lines of '80% of the time, the witnesses are correct, and the other 20% of the time, witnesses give a random answer', then the probability would be 97% (an 80% chance that the witness was correct, and an additional 20%x85%=17% chance that the witness should be ignored, but that the taxi was blue anyway).
Strange problem or bad wording
