Why does the order of events A and B not matter with conditional probability? p(A | B) x p(B) = p(B | A) x p(A) Please can someone explain why the order of events with conditional probability does not matter?
p(A and B) = p(A | B) x p(B) = p(B | A) x p(A)
 A: I think you are asking a pretty good question despite seeming innocent at first. My answer would be that, from a matehmatical point of view, "B given A" or "B/A" does not necesarelly mean that A happened before B.
A could have happened before, after or at the same time as B, and causal relationships between A and B could go either way, but what P(B/A) really means is "OK: We know A happened/is happening/will happen, now what is the chance that B happenned/is happening/will happen as well?"
In these terms, keep in mind that we don't know everything that happenned in the past, neither do we ignore everything that will happen in the future.
Silly example: I am going to roll two dice. In experminet A I throw one of them first, getting a 4. What is the probability of the sum of both dice being 9? In case B, I have not rolled any of the dice yet, but I know the second one is rigged and it will always be a 4. What is the probability of the sum of both dice being 9 now? Of course the same as before!
