The probability that a random ball is contained in a given ball
Uwe Saint‐Mont · Journal of Interdisciplinary Mathematics · 2004
Denote by Bn(R) a ball of radius R in n -dimensional space. Successively choose points C, A ∈ Bn(R) at random. Then the probability that the n -dimensional ball Bn(C, AC) , having center C and radius AC , is entirely contained in Bn(R) is n!n!=(2n)! . The result holds for every metric and . It can be generalized to n -dimensional cubes in n -dimensional cuboids.