  The theorem developed by John Bell constituted the starting point of a
revolution that translated a philosophical question about the nature of reality
into the broad and intense field of research of the quantum information
technologies. We focus on a system of two qubits prepared in a random, mixed
state, and we study the typical behavior of their nonlocality via the
CHSH--Bell inequality. Afterward, motivated by the necessity of accounting for
inefficiency in the state preparation, we address to what extent states close
enough to one with a high degree of nonclassicality can violate local realism
with a previously chosen experimental setup.
