We have a stick of unit length, and we consider breaking it in three pieces using one of the following three methods. 1. We choose randomly and independently two points on the stick using a uniform PDF, and we break the stick at these two points.
2. We break the stick at a random point chosen by using a uniform PDF, and then we break the larger of the two pieces at a random point chosen by using a uniform PDF.
For each of the methods above, what is the probability that the three pieces we are left with can form a triangle?