  An analysis is made within the quantum formalism of the probabilistic
features of the electron spin correlation, with the purpose of clarifying the
concepts of contextuality and measurement dependence. The quantum formulas for
the spin correlation are then derived on the basis of a probability
distribution function and its associated geometric representation, both for a
pair of projections of a single-particle spin and for the bipartite system in
singlet spin state. This endows the spin correlation with a clear probabilistic
meaning and leaves the door open for a possible physical image of the electron
spin, as discussed at the end of the paper.
