  It is shown that the probabilities for the spin singlet can be reproduced
through classical resources, with no communication between the distant parties,
by using merely shared (pseudo-)randomness. If the parties are conscious beings
aware of both the hidden-variables and the random mechanism, then one has a
conspiracy. If the parties are aware of only the random variables, they may be
induced to believe that they are able to send instantaneous information to one
another. It is also possible to reproduce the correlations at the price of
reducing the detection efficiency. It is further demonstrated that the same
probability decomposition could be realized through action-at-a-distance,
provided it existed.
