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 | Comment 3 of 20 |
P(at least one car) = 1 - P(no cars)

So the probability of no cars in 20 minutes = 1 - 609/625 = 16/625

There are four 5-minute intervals in 20 minutes. Assuming they are independent, P(no cars in 20 min.) = P(no cars in 5 minutes)^4
P(no cars in 5 min) = 2/5

The probability of at least one car is then 3/5.

I think the independence assumption is probably not valid in the real world, but the problem seems to indicate we can.

  Posted by Jer on 2004-04-09 12:13:22
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