  We show that the convex set of separable mixed states of the 2 x 2 system is
a body of constant height. This fact is used to prove that the probability to
find a random state to be separable equals 2 times the probability to find a
random boundary state to be separable, provided the random states are generated
uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An
analogous property holds for the set of positive-partial-transpose states for
an arbitrary bipartite system.
