Abstract: In 2022, the Nobel prize in physics award researches on the nonlocal quantum entanglement and basic test of Bell inequalities. Under this background, this paper aims to analysis various non-locality in quantum mechanics, to derive the Bell inequality satisfied by conditional probability, and further to understand the nature of violation of Bell inequalities in quantum mechanics．

Key words:  quantum nonlocality, EPR paradox, local hidden variable, quantum entanglement, bell inequality