Is the rule: P(AB I) = P(BA I) (which is used to derive Bayes rule) an axiom for probability? And if so, do you guys find it intuitive that it should hold. For instance consider a box with green and red beads. Do you think it is strictly obvious that the probability of getting red-green is the same as the probability for getting green-red? My question is because I do not think that Bayes rule is intuitive yet it is derived from exactly this principle.