, Volume 16, Issue 4, pp 567–573 | Cite as

The probability thatn random points in a triangle are in convex position

  • Pavel Valtr


We show thatn random points chosen independently and uniformly from a triangle are in convex position with probability
$$\frac{{2^n (3n - 3)!}}{{((n - 1)!)^3 (2n)!}}$$

Mathematics Subject Classification (1991)

Primary: 60 D 05 Secondary: 52 A 22 


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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • Pavel Valtr
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic

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