hey, can anyone help me to proof the probability, thankp(B|C)=P(B|~C), where ~c mean "not c"?

Answer 1

You haven't told us what you're trying to prove.

However, if p(B|C) = p(B|C*), where C* means "not C", then events B and C are independent of each other.

The equation states that the probability of B given that C happened is the same as the probability of B given that C did not happen. Thus the probability of B does not depend on C.