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

Home > Probability
Cars on the road (Posted on 2004-04-09) Difficulty: 2 of 5
If the probability of observing a car (read: at least one car) in 20 minutes on a highway is 609/625, what is the probability of observing a car (read: at least one) in 5 minutes (assuming constant default probability)?

See The Solution Submitted by SilverKnight    
Rating: 2.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): Auto-suggestion | Comment 6 of 20 |
(In reply to re(2): Auto-suggestion by ThoughtProvoker)

The Poisson distribution is the standard one for arrivals of independent events such as telephone calls.  If we do assume Poisson for this problem then the probability that, in time t, k cars have passed by is given by  (Lt)^k*exp(-Lt)/k!  where L is to be determined from the data of the problem. The probability that at least one car has passed in time T is clearly 1-exp(-LT).  Hence 20L is determined by exp(-20L) = 16/625, so that L = -(1/20)log(16/625) and then using this L we compute the probability that at least one car has passed by in 5 minutes as 1-exp(-5L) which works out to be 1 minus the 4th root of 16/625 or 3/5 (surprise!).
  Posted by Richard on 2004-04-09 14:28:47

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 (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information