Why is P(A∩B)/P(B) called conditional probability? Or, let's turn it the other way round (which is your question), why would conditional probability be given by P(A∩B)/P(B)? I think I was able to develop a proof, see below. Of course, double-checking by others would be required.
First, I would define conditional probability as the “Probability of A knowing that B occurs”, which is meaningful and I guess everybody would agree on (see also wikipedia).
Starting from there, “Probability of A knowing that B occurs” means the probability of A in a restricted space... (read more)
Why is P(A∩B)/P(B) called conditional probability? Or, let's turn it the other way round (which is your question), why would conditional probability be given by P(A∩B)/P(B)? I think I was able to develop a proof, see below. Of course, double-checking by others would be required.
First, I would define conditional probability as the “Probability of A knowing that B occurs”, which is meaningful and I guess everybody would agree on (see also wikipedia).
Starting from there, “Probability of A knowing that B occurs” means the probability of A in a restricted space... (read more)