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

Home > Probability
Two random points (Posted on 2018-04-26) Difficulty: 3 of 5
On a circumference of a given circle with a radius R two random points A & B are independently chosen.

What is the probability of AB being less than R ?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution | Comment 1 of 10
For convenience create a coordinate system with the origin at the center of the circle and (1,0)=A

B is at some angle from -180 to 180 from A with uniform probability.  AB is only closer than R if the angle is between -60 and 60.

Thus the probability is 120/360 = 1/3.

  Posted by Jer on 2018-04-26 09:50:49
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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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