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Usenet Newsgroups : rec.puzzles Hall of Fame


The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

   
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Categories : probability : cab.p

A cab was involved in a hit and run accident at night.  Two cab companies,
the Green and the Blue, operate in the city.  Here is some data:

	a)  Although the two companies are equal in size, 85% of cab 
accidents in the city involve Green cabs and 15% involve Blue cabs.

	b)  A witness identified the cab in this particular accident as Blue.
The court tested the reliability of the witness under the same circumstances
that existed on the night of the accident and concluded that the witness 
correctly identified each one of the two colors 80% of the time and failed
20% of the time.

What is the probability that the cab involved in the accident was 
Blue rather than Green?

If it looks like an obvious problem in statistics, then consider the
following argument:

The probability that the color of the cab was Blue is 80%!  After all,
the witness is correct 80% of the time, and this time he said it was Blue!

What else need be considered?  Nothing, right?

If we look at Bayes theorem (pretty basic statistical theorem) we 
should get a much lower probability.  But why should we consider statistical
theorems when the problem appears so clear cut?  Should we just accept the 
80% figure as correct?


Solution


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