  The basic Leggett inequalities, i.e. those inequalities in which the
particular assumptions of Leggett's hidden-variable model (e.g. Malus law) were
not yet introduced, are usually derived using hidden-variable distributions of
probabilities (although in some cases completely general, positive
probabilities would lead to the same result). This fact creates sometimes the
illusion that these basic inequalities are a belonging of the hidden-variable
theories and are bound to contradict the quantum theory. In the present text
the basic Leggett inequalities are derived in the most general way, i.e. no
assumption is made that the distribution of probabilities would result from
some wave function, or from some set of classical variables. The consequence is
that as long as one and the same probability distribution is used in the
calculus of all the averages appearing in the basic Leggett inequalities, no
contradiction may occur. These inequalities may be violated only when different
averages are calculated with different distributions, for example, some of them
calculated with the quantum formalism and the others with some distribution of
classical parameters.
