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?
B=The car is blue.
~B=The car is not blue.
X=The person says that it is blue.
~X=The person says that it is not blue.
Therefore, there is a 95.77% chance that the car is blue, given that the person said that it was blue.
Edited on September 23, 2011, 4:01 pm
Posted by Math Man
on 2011-09-23 16:00:41