What is the probability that when a stick is broken into 3 pieces that a triangle can be formed. Assume the 2 breaks to occur at the same time and are independent of each other.
Let A and B the randomly selected points on [0,1]. Assume B>A for beginning.
Triangular inequalities will reveal:
A<1/2 and
B>1/2 and
B-A<1/2
I am skipping several steps here but due to conditional probability that should be equivalent to:
$\displaystyle
\int_{1/2}^{1} (x-1/2) dx \;=\frac{1}{8}
$
We also have the symmetric case where A>B. So,
the answer = 2 * 1/8 = 1/4
-O believes.