Math So Hard It Can Break You

(I rather impressively snapped my arm in half in gym class, so badly that it looked like I had an extra elbow. It looked incredibly scary and ended up being the talk of the school, but it was a clean break and the hospital was able to fix it perfectly. I was in a cast for the next few months, during which this happens:)

Math Teacher: “Every year I talk about a stick for this question, but given recent events… If you broke [My Name]’s arm into three randomly-sized pieces, what is the probability that they can form a triangle?”