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

 I've a broken stick (Posted on 2003-12-07)
I've a straight stick which has been broken into three random-length pieces.
What is the probability that the pieces can be put together to form a triangle?
If not, perhaps this will help: here are several methods to break the stick into the three random length pieces:
1. I select, independently, and at random, two points from the points that range uniformly along the stick, then break the stick at these two points.
2. I select one point, independently, and at random (again uniformly), and break the stick at this point. I then randomly (with even chances) select one of the two sticks and randomly select a point (again uniformly) along that stick, and break it at that point.
3. I select one point, independently, and at random (again uniformly), and break the stick at this point. I then select the larger stick, and randomly select a point (again uniformly) along that stick, and break it at that point.
If this clarifies the problem, please show how this affects your work.

 No Solution Yet Submitted by SilverKnight Rating: 3.6000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): help me! correction | Comment 7 of 26 |
(In reply to re: help me! by Penny)

My mistake, typo, it was supposed to say
p(a*,b* both>0.5) = ¼
i.e. both your arbitrary points are more than half-way up the stick making piece a >0.5
It should then go on to say,
".....p(a*,b* both<0.5) = ¼ (making c>0.5)
p(a*<0.25 and b*>0.75)= ¼ (making b>0.5)
so probability you can make a triangle is ¼ "

 Posted by Lee on 2003-12-08 02:54:03

 Search: Search body:
Forums (0)