  In previous studies, we have explored the ansatz that the volume elements of
the Bures metrics over quantum systems might serve as prior distributions, in
analogy to the (classical) Bayesian role of the volume elements ("Jeffreys'
priors") of Fisher information metrics. Continuing this work, we obtain exact
Bures probabilities that the members of certain low-dimensional subsets of the
fifteen-dimensional convex set of 4 x 4 density matrices are separable or
classically correlated. The main analytical tools employed are symbolic
integration and a formula of Dittmann (quant-ph/9908044) for Bures metric
tensors. This study complements an earlier one (quant-ph/9810026) in which
numerical (randomization) --- but not integration --- methods were used to
estimate Bures separability probabilities for unrestricted 4 x 4 or 6 x 6
density matrices. The exact values adduced here for pairs of quantum bits
(qubits), typically, well exceed the estimate (.1) there, but this disparity
may be attributable to our focus on special low-dimensional subsets. Quite
remarkably, for the q = 1 and q = 1/2 states inferred using the principle of
maximum nonadditive (Tsallis) entropy, the separability probabilities are both
equal to 2^{1/2} - 1. For the Werner qubit-qutrit and qutrit-qutrit states, the
probabilities are vanishingly small, while in the qubit-qubit case it is 1/4.
