All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
A blue taxi II (Posted on 2013-03-08) Difficulty: 3 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 1 of 4

Bayes' Theorem:

p(blue given reported blue)
  = p(blue and reported blue) / p(reported blue)
  = .85 * .8 / (.85 * .8 + .15 * .2 * 1/(n-1))
  = 17/25 / (17/25 + 3/(100*(n-1)))
  = 17 / (17 + 75/(100*(n-1)))


  Posted by Charlie on 2013-03-08 13:21:39
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information