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Medium · Probability & Statistics · Quant Trader interview question · probability, geometry, triangle-inequality, uniform-distribution
You are a lumber trader. A client brings you a wooden stick of length 1. He asks you to break the stick at two uniformly random points. What is the probability that the three resulting pieces can form a triangle? Remember, for three segments of length $a$, $b$, and $c$ to form a triangle, the triangle inequality must hold: $a + b > c$, $a + c > b$, and $b + c > a$.