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

Home > Probability
Don't Be a Square (Posted on 2003-05-19) Difficulty: 4 of 5
Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?

See The Solution Submitted by DJ    
Rating: 4.4667 (15 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Numerical Answers | Comment 10 of 21 |
(In reply to Numerical Answers by Charlie)

The algorithm I originally posted produces a distorted portion of the probability distribution above 180 degrees, but that below 180 degrees is unaffected so the probablities shown should still be accurate within the limitations of numerical integration.

The problem is exemplified by a span of 2 points spaced 170 degrees apart. The algorithm assumes an incremental probability that this would expand, with the third point, to, say, 250 by that third point being external to the original pair and 80 degrees from one of them. However, the distance between the original two is still 170, leaving an occupied span of 360 - 170 = 190 degrees.

This possibility of the new point flipping the occupied span to the opposite side again affects only the distribution within the part above 180 degrees, and not the probability of 180 or less versus 180 or more.
  Posted by Charlie on 2003-05-19 17:59:22

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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information