  We derive a Bell-like inequality involving all correlations in local
observables with uncertainty free states and show that the inequality is
violated in quantum mechanics for EPR and GHZ states. If the uncertainties are
allowed in local observables then the statistical predictions of hidden
variable theory is well respected in quantum world. We argue that the
uncertainties play a key role in understanding the non-locality issues in
quantum world. Thus we can not rule out the possibility that a local, realistic
hidden variable theory with statistical uncertainties in the observables might
reproduce all the results of quantum theory.
