  This paper shows how the classical finite probability theory (with
equiprobable outcomes) can be reinterpreted and recast as the quantum
probability calculus of a pedagogical or "toy" model of quantum mechanics over
sets (QM/sets). There have been four previous attempts to develop a
quantum-like model with the base field of $\mathbb{C}$ replaced by
$\mathbb{Z}_{2}$, but they are all forced into a merely "modal" interpretation
by requiring the brackets to take values in $\mathbb{Z}_{2}$ (1 = possible, 0 =
impossible). But the usual QM brackets <{\psi}|{\phi}> give the "overlap"
between states {\psi} and {\phi}, so for subsets S,T of U, the natural
definition is $<S|T>=|S{\cap}T|$. This allows QM/sets to be developed with a
full probability calculus that turns out to be the perfectly classical
Laplace-Boole finite probability theory. The point is not to clarify finite
probability theory but to elucidate quantum mechanics itself by seeing some of
its quantum features (e.g., two-slit experiment) in a classical setting.
