Random cuts make a triangle?

On 12/5/15, @mburnsmath posted the following classical problem: Break a piece of spaghetti into two pieces so that they are different lengths. Take the longer of the two pieces and break it into two pieces that are different elngths. This leaves you with three pieces of spaghetti. What is the probability that the three pieces can form a triangle? This is an attempt to show why the solution is greater than 1/3. Not seeing red below? GeoGebra is not cooperating. View a better image.