Bell's theorem proves the incompatibility between quantum mechanics and local realistic hidden-variable theories. In this paper we first show that, contrary to a common belief, the theoretical proof of Bell's theorem is not affected by counterfactual reasoning. Second, we show that the experimental verification of this theorem may be affected by our unavoidable ignorance about the probability distribution of the hidden variables. Our study is based on the standard theory of random variables, and lays the groundwork for a critical rethinking of Bell's theorem and its consequences.