The Broken Stick Problem.

You've got a stick. Two points are chosen independently and at a random on the stick. The stick is broken at those points to form three smaller sticks. What is the probability these three sticks can form a triangle?

Apparently this problem has a pedigree that goes back to 1854 examination at Cambridge University.
When you're ready for a neat solution. Here.
A more traditional solution is here.
And MIT Blossoms also has a video and teacher resources here