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A blue taxi (Posted on 2002-05-24) Difficulty: 4 of 5
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?

See The Solution Submitted by levik    
Rating: 3.7857 (14 votes)

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Solution Blue's Clues Comment 17 of 17 |
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.
P(B&X)=0.85(0.8)=0.68
P(B&~X)=0.85(0.2)=0.17
P(~B&X)=0.15(0.2)=0.03
P(~B&~X)=0.15(0.8)=0.12
P(X)=0.68+0.03=0.71
P(B|X)=0.68/0.71=68/71=0.9577
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

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