A note on the volume of a random polytope in a tetrahedron (Q1071263)

Denote by \(V_ n\) the expected volume of the convex hull of \(n\) points chosen independently and uniformly from a tetrahedron of unit volume. It is shown that \(1 - V_ n \sim (3/4)(\log n)^ 2/n\) as \(n\) tends to infinity. Additionally, the paper contains a remark to a result of \textit{G. R. Hall} [J. Appl. Probab. 19, 712--715 (1982; Zbl 0492.60014)] concerning the probability that a random triangle is acute.