  The frame of classical probability theory can be generalized by enlarging the
usual family of random variables in order to encompass nondeterministic ones:
this leads to a frame in which two kinds of correlations emerge: the classical
correlation which is coded in the mixed state of the physical system and a new
correlation, to be called probabilistic entanglement, which may occur also at
pure states. We examine to what extent this characterization of correlations
can be applied to quantum mechanics. Explicit calculations on simple examples
outline that a same quantum state can show only classical correlations or only
entanglement depending on its statistical content; situations may also arise in
which the two kinds of correlations compensate each other.
