Broken Stick Triangle - Quant Trader Interview Question
Difficulty: Medium
Category: Probability & Statistics
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: probability, geometry, triangle-inequality, uniform-distribution
Problem Description
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 $b + c > a$.
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