There are n taxi firms in Carborough (n > 1), each one using a different color for its taxis.

A crime has occured in Carborough, involving a taxi. The police interviewed an eyewitness, who stated that the taxi involved was blue.

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. In other words, faced with a blue taxi 20% of witnesses say it is some other color, chosen at random from the remaining n - 1 possible choices. Also, faced with a non-blue taxi, the 80-20 rule is still applicable.

If 85% of the taxis in Carborough are blue, determine the probability (in terms of n) that the taxi involved in the crime was actually blue.

(In reply to Solution- independent of n by Dan Rosen)

The problem with the table is the line

B               O                      0.2x0.85 = 0.03

When the color is other than blue, blue is not the only color that might be reported, but some third color.

Incidentally also you show a line:

 O               O                     0.8x0.15 = 0.12

implying that when the taxi is other than blue, a correct identification is the only way to get a report of another color. But it could be a different other color, and be part of the wrong set.

Posted by Charlie on 2013-03-13 08:37:16