  The question concerning the physical realizability of a probability
distribution is of quite importance in Quantum foundations. Specker first
pointed out that this question cannot be answered from Kolmogorov's axioms
alone. Lately, this observation of Specker has motivated simple principles
(exclusivity principle/ local orthogonality principle) that can explain quantum
limit regarding the possible sets of experimental probabilities in various
nonlocality and contextuality experiments. We study Specker's observation in
the simplest scenario involving three inputs each with two outputs. Then using
only linear constraints imposed on joint probabilities by this principle, we
reveal unphysical nature of Garg-Mermin (GM) correlation. Interestingly, GM
correlation was proposed to falsify the following suggestion by Fine: if the
inequalities of Clauser and Horne (CH) holds, then there exists a deterministic
local hidden-variable model for a spin-1/2 correlation experiment of the
Einstein-Podolsky-Rosen type, even when more than two observables are involved
on each side. Our result establishes that, unlike in the CH scenario, the local
orthogonality principle at single copy level is not equivalent to the
no-signaling condition in the GM scenario.
