 It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the “quantum logic” of projection operators on a Hilbert  space.[1]  Moreover, the usual statistical interpretation of quantum mechanics asks us to take this generalized quantum probability theory quite literally—that is, not as merely a formal analogue of its classical counterpart, but as a genuine doctrine of chances. In this section, I survey this quantum probability theory and its supporting quantum  logic.[2]