  We extend a well-known theorem of Murski\v{\i} to the probability space of
finite models of a system $\mathcal{M}$ of identities of a strong idempotent
linear Maltsev condition. We characterize the models of $\mathcal{M}$ in a way
that can be easily turned into an algorithm for producing random finite models
of $\mathcal{M}$, and we prove that under mild restrictions on $\mathcal{M}$, a
random finite model of $\mathcal{M}$ is almost surely idemprimal. This implies
that even if such an $\mathcal{M}$ is distinguishable from another idempotent
linear Maltsev condition by a finite model $\mathbf{A}$ of $\mathcal{M}$, a
random search for a finite model $\mathbf{A}$ of $\mathcal{M}$ with this
property will almost surely fail.
