  Compelling evidence-though yet no formal proof--has been adduced that the
probability that a generic two-qubit state ($\rho$) is separable is
$\frac{8}{33}$ (arXiv:1301.6617, arXiv:1109.2560, arXiv:0704.3723). Proceeding
in related analytical frameworks, using a further determinantal moment formula
of C. Dunkl (Appendix), we reach the conclusion that one-half of this
probability arises when the determinantal inequality $|\rho^{PT}|>|\rho|$,
where $PT$ denotes the partial transpose, is satisfied, and, the other half,
when $|\rho|>|\rho^{PT}|$. These probabilities are taken with respect to the
flat, Hilbert-Schmidt measure on the fifteen-dimensional convex set of $4
\times 4$ density matrices. We find fully parallel bisection/equipartition
results for the previously adduced, as well, two-"re[al]bit" and
two-"quater[nionic]bit"separability probabilities of $\frac{29}{64}$ and
$\frac{26}{323}$, respectively. The computational results reported lend strong
support to those obtained earlier--including the "concise formula" that yields
them--most conspicuously amongst those findings being the $\frac{29}{64},
\frac{8}{33}$ and $\frac{26}{323}$ probabilities noted.
