1. ## probability question

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

2. The 1 meter length is unimportant.
I assume we're making two cuts uniformly distributed along the bar.
So let $X_1$ and $X_2$ 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 $X_1$, $X_2-X_1$ and $1-X_2$,
BUT here I'm assuming $X_2>X_1$ which is really the order stats.
I'm trying to figure the logic here.
We need $P(max\{X_1,X_2-X_1,1-X_2\}<.5)$
The joint density of these two is $f(x_1,x_2)=2I(0

3. 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?

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.