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?
(In reply to re: A more paradoxical version.
I disagree. If the person said that the taxi was green, and witnesses are right 80% of the time, then the probability that it was green has to be at least 80%. If the witnesses are straight out wrong the other 20%, then the probability is exactly 80%. If, as friedlinguini suggested, they say random things 20% of the time, then there is 80% + (20% * 15%) = 83% chance.
Edited on September 9, 2003, 4:09 pm
Posted by Sam
on 2003-09-09 16:08:50