Misunderstandings for Bell's Inequality

It is pointed that Bell had two misunderstandings for his work: Firstly,the hidden variable theory that he applied for deriving Bell's inequality keeps wholly intact the operating rules of classical probabilistic theory,but he regarded it as the general local hidden variable theory.Secondly,in Bell's work,the promise actually deriving Bell's inequality is not the one that Bell regarded as the character of local hidden variable theory.Also,other versions can prove Bell's inequality without local hidden variable theory and the Lochak's objection against Bell's theory are examined.