  We revisit the computation of correlations of spin projections onto unit
vectors for spin-1/2 particles in Quantum Mechanics. We then choose one of the
Boole inequalities that, as we recall, must be obeyed by collections of
sequences of normalized spin-1/2 projections onto unit vectors that belong to,
say, the plane that is orthogonal to the classical trajectory or to the three
dimensional space. Next we define the concept of being a-p for i-indexed
sequences of spin-1/2 particles: it turns out that a sequence of spin-1/2
particles is a-p if and only if the particles behave as if they had indeed been
prepared (in the usual sense) to have definite spins +1 or -1 along the axis a,
the sequence of signs being pre-determined. The a-p property is formulated in a
way abstract enough to let one generalize it and we define the concept of being
a-p and b-p. However, using our chosen Boole inequality we prove that no
particle sequence can be both a-p and b-p when a and b are not co-linear. We
next consider two modifications of Quantum Mechanics:
  - The first one by assuming both Weak Realism, the weakest form of Realism
needed to develop any main theorem in Bell's Theory, and Locality. - The second
one by assuming Weak Realism and an hypothesis that turns out to be none else
than (relativistic) Causality extended to cover as well the observable values
that make sense only if one assumes Weak Realism. In both cases we arrive at
the conclusion that in the EPRB setting where successive pairs of spin-1/2
particles are prepared in the so-called singlet state, one of these particles
sequences is both a-p and b-p and a and b are the opposite of the vectors
respectively used to project the spin of the other particle and to get the
Realism-based alternate value for a projection. Thus the usual discussions of
Bell's inequalities under such hypotheses do not even make physical sense.
