Thread: probability question

what's the probability a 1 meter steel broke into 3 pieces that forms a triangle

The 1 meter length is unimportant.
I assume we're making two cuts uniformly distributed along the bar.
So let and be iid U(0,1) rvs.
I checked the three case and each case we want the largest cut to be less than .5.
The cuts are , and ,
BUT here I'm assuming which is really the order stats.
I'm trying to figure the logic here.
We need
The joint density of these two is

is that means Pr(one piece<0.5)=1/2 and the other two we regard them as a whole
umm.. do u mean it's 1/4?

Originally Posted by camilla_xu

what's the probability a 1 meter steel broke into 3 pieces that forms a triangle

It will depend on how the stick is broken.

Read the attachment and these:

Stick Broken Into Three Pieces. Solution in Trilinear Coordinates from Interactive Mathematics Miscellany and Puzzles

Random Triangles

Problem 8: Random Triangles and an Introduction to Density

Mathematical Recreations and Essays - Google Book Search

Thanks, I was googling Buffon at 2 :30 am but couldn't find this.