Breaking the Stick

What this geometric probability question tests

This is a classic easy-to-medium difficulty probability problem that asks you to combine uniform random selection with a geometric constraint. It rewards clear problem setup and the ability to visualize a continuous sample space rather than brute-force calculation.

The core skill is translating a physical constraint—the triangle inequality—into inequalities on your random variables, then finding the region of the unit square (or simplex) where all constraints hold simultaneously. Candidates who solve this cleanly typically sketch the feasible region and compute its area directly, rather than attempting integration without a visual anchor.

• Uniform distribution on continuous domains
• Triangle inequality and its implications
• Geometric probability and area ratios
• Symmetry and coordinate transformations