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.)
Solution Auto-suggestion | Comment 2 of 20 |

(The mention of cars in this puzzle, made me think of all the poor dogs who are run over every day by cars. How sad. Someone should take up some donations for these dogs.)

As usual, Ady is correct. The odds of seeing one or more cars in time period T, is 1 minus the odds of not seeing any cars in time period T. The probability of not seeing any car in  20 minutes is the product of the probabilities not seeing a car in four successive 5 minute intervals: 1 - p^4, if 'p' is the probability of non-seeing in 5 minutes.  If 1 - p^4 = 609/625, then p^4 = 16 / 625, so p = 2/5.  The probability of seeing one or more cars in 5 minutes is then 1 - p, or 3/5.

If the problem had asked for the odds of seeing exactly one car in 5 minutes, the problem would have been a lot more difficult.  

  Posted by Penny on 2004-04-09 12:01:02
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information