Probability of forming a polygon from a stick with $n$ breaks We have a stick of length one which is broken into $n$ pieces.  What is the probability that a quadrilateral can be formed from the broken pieces? 
I know the answer for $n=4$ as it is the probability that none of the pieces are above $0.5$ in length, that is $1/2$. 
Does anyone see what the probability is generally or what it is for any case greater than four?  

The probability you can form a closed polygon is the probability that no segment has length greater than $1/2$.
