  In this work we aim to analyze the Clauser-Horne-Shimony-Holt CHSH inequality
strictly in the context of probability theory. In the course of assembling
inequality we have to take care not to produce assumptions a priori, that is,
physically or intuitively accepted suppositions. Of course, this does not mean
that after these considerations, we put the adequate physical conditions
suitable and generally accepted in these contexts. This allows us to clearly
visualize the possibility of finding a greater inequality than that of CHSH in
which it is included. This inequality does not contradict the CHSH inequality.
This result is suported by using a robust computational simulation, showing the
possibility for obtaining an inequality for quantum mechanics that is not
violated and allows random hidden variables without any conflict with Bell's
inequality.
