  The high degree of symmetry renders the dynamics of cosmological as well as
some black hole spacetimes describable by a system of finite degrees of
freedom. These systems are generally known as minisuperspace models. One of
their important key features is the invariance of the corresponding reduced
actions under reparametrizations of the independent variable, a fact that can
be seen as the remnant of the general covariance of the full theory. In the
case of a system of $n$ degrees of freedom, described by a Lagrangian quadratic
in velocities, one can use the lapse by either gauge fixing it or letting it be
defined by the constraint and subsequently substitute into the rest of the
equations. In the first case, the system is solvable for $n$ accelerations and
the constraint becomes a restriction among constants. In the second case, the
system can only be solved for $n-1$ accelerations and the "gauge" freedom is
transferred to the choice of one of the scalar degrees of freedom. In this
paper, we take the second path and express all $n-1$ scalar degrees of freedom
in terms of the remaining one, say $q$. By considering these $n-1$ degrees of
freedom as arbitrary but given functions of $q$, we manage to extract a two
dimensional pure gauge system consisting of the lapse $N$ and the arbitrary
$q$: in a way, we decouple the reparametrization invariance from the rest of
the equations of motion. The solution of the corresponding quantum two
dimensional system is used for the definition of a generalized probability for
every configuration $f^i (q)$, be it classical or not. The main result is that,
interestingly enough, this probability attains its extrema on the classical
solution of the initial $n$-dimensional system.
