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.)
Web Research | Comment 20 of 21 |
A search for probability points semicircle yields a page ( asking about such problems in various dimensions, but including a statement about the two-dimensional case (actually 1-dimensional considered along the circumference):

"The case n = 0 yields the known probability that all k points lie on a semicircle: k/2^(k-1)."

In fact the formula k/2^(k-1) fits with both the numerical integration solution as well as the simulation.

Only my estimate that the value .03513 for 9 points, which I took as 1/32, really should have been 9/256.

The .01951 for 10 points is close to the 10/512 theory predicts.
  Posted by Charlie on 2003-05-23 03:51:22
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