On the probability of forming polygons from a broken stick

William Verreault

Statistics & Probability Letters, 2022, vol. 180, issue C

Abstract: Break a stick at random at n−1 points to obtain n pieces. We give an explicit formula for the probability that every choice of k segments from this broken stick can form a k-gon, generalizing similar work. The method we use can be applied to other geometric probability problems involving broken sticks, which are part of a long-standing class of recreational probability problems with several applications to real-world models.

Keywords: Geometric probability; Broken stick; Order statistics; Spacings (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109237

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