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Difficulty: Medium
Category: Conditional Probability
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Topics: probability, geometry, triangle-inequality, uniform-distribution
A trader is given a stick of length 1. They break the stick at two points chosen uniformly at random. What is the probability that the three resulting pieces can form a triangle? Constraints: - The two break points are chosen independently and uniformly at random along the length of the stick. - A triangle can be formed if and only if the length of each piece is less than 0.5.
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