perplexus.info :: Probability : A blue taxi

A blue taxi (Posted on 2002-05-24)

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?

Submitted by levik

Rating: 3.7857 (14 votes)

Solution: (Hide)

Let's say the city has a total of 100 taxis (this way we can have a one to one relationship between taxis and percent).
Of these 100, 85 are blue, and 15 are green. Let's look at both cases:
85/100 blue taxi is involved. Since the witness will be wrong 20% of the time, they will say they saw a blue taxi 68 times, and claim that the taxi was green the other 17 times.
15/100 green taxi is involved. 12 witnesses would correctly identify a green taxi, but 3 would wrongly claim to have seen a blue one.
We know that the witness said they saw a blue taxi. There is a total of 68+3 = 71 percent chance for that to happen. Of those 71%, 68% of the time the taxi will in truth be blue. Thus the probability of the taxi being blue is 68/71 = approximately 95.8%

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Blue's Clues	Math Man	2011-09-23 16:00:41
Puzzle Solution	K Sengupta	2008-11-15 13:53:35
Answer	K Sengupta	2008-10-08 00:27:21
re: kind of on the same lines......	Charlie	2007-02-21 09:39:17
kind of on the same lines......	sean	2007-02-20 23:17:08
re(2): A more paradoxical version.	Sam	2003-09-09 16:08:50
re: A more paradoxical version.	fwaff	2003-03-27 06:30:37
A more paradoxical version.	Charlie	2003-03-26 14:09:57
Re: answer 2	levik	2002-05-28 11:33:12
Am I making this too simple?	Carey	2002-05-28 10:30:47
ANSWER 2	Dulanjana	2002-05-28 01:14:58
ANSWER	Dulanjana	2002-05-27 23:58:38
Response	TomM	2002-05-25 04:15:37
Solution, and Why Previous Comments are Wrong	Jim Lyon	2002-05-24 08:00:36
Strange problem or bad wording	friedlinguini	2002-05-24 07:16:19
re: interesting reversal	levik	2002-05-24 06:50:56
interesting reversal	TomM	2002-05-24 05:18:48

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