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 you can answer this at this point, please do.
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.

I hate to bring back a 2-year old topic, i know it's not good to do it in any forum, but i think it's better than creating a new topic about the same subject...
Anyway, Charlie, on your solution, after the integration you divide the result by 1/2. I didn't get the reason of this...

Posted by Jefferson on 2006-09-22 23:42:16