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

Home > Probability
Three Points in a Square (Posted on 2008-03-17) Difficulty: 3 of 5
Three points are chosen at random inside a square. Each point is chosen by choosing a random x-coordinate and a random y-coordinate.

A triangle is drawn with the three random points as the vertices. What is the probability that the center of the square is inside the triangle?

No Solution Yet Submitted by Brian Smith    
Rating: 3.2000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips thoughts to share with ed bottemiller | Comment 8 of 18 |
(In reply to re: Faster, simpler, better by ed bottemiller)

hi ed,

it's vital to have good hunches to serve as guidelines for where to invest work.

was your notion about the "average" inscribed triangle would have area one quarter that of the framework square such an insight? im not sure. my guess is that finding the average area of a triangle inside a unit square (or, more simply, inside a unit circle) is a different problem, and may well result in something other than 1/4. certainly the average for the unit circle case is less than the average for the unit square case, unlike the situation with this problem, where we've seen the results to be identical.


  Posted by FrankM on 2008-03-17 21:47:34
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 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information