Let G be a finite group of order n and S be a subset of G not containing the identity element of G. Let p (0 < p < 1) be a fixed number. The authors define the set of all labelled Cayley digraphs X(G, S) (S ≤ G|{1}) of G as a simple space and assign a probability measure by requiring P(a ∈ S) = p for any a ∈ G|{1}. Here it is shown that the probability of the set of Cayley digraphs of G with diameter 2 approaches 1 as the order n of G approaches infinity.
