Probabilistic Estimates of Rubik's Cube Group Diameters

A modified version of the coupon collector's problem in probabilistic theory can accurately predict the diameters of the 2x2x2 and 3x3x3 Rubik's Cubes in the quarter-turn metric, and provides estimates for the diameters of the 4x4x4 and 5x5x5 Cubes.