Probability that n random points are in convex position

Pavel Valtr Department of Applied Mathematics Charles University Czech Republic email: valtr@CSPGUK11.bitnet Report B 94-01 January 94

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We show that $n$ random points chosen independently and uniformly from a parallelogram are in convex position with probability $$\left({{2n-2\choose n-1}\over n!}\right)^2.$$