The histories interpretation of quantum mechanics employs probability theory in exactly the same way as in the other sciences once a sample space \(\SC\) has been specified. A quantum sample space \(\SC\) is always a projective decomposition of the identity operator \(I\), hereafter referred to as a “projective decomposition” (or “decomposition”), on the quantum Hilbert space \(\HC\) used to model the situation of interest. That is to say, a collection \(\{P_j\}\) of projectors (\(P^{}_j = P_j^\dagger =P_j^2)\) which are mutually orthogonal (\(P_jP_k = 0\) for \(j\neq k\)) and sum to the identity