From the product rule it is possible to derive Bayes' rule:

(1) |

If we assume that

Before making the observation *B*, the learning system knows only *C*,
but afterwards it knows *BC*, that is, it knows ``*B* and *C*''.
Bayes' rule then tells how the learning system should adapt *P*(*A* | *C*)into *P*(*A* | *BC*) in response to the observation. In order for Bayes'
rule to be useful, the explanation *A* needs to be such that together
with the prior assumptions and experience *C* it fixes the probability
*P*(*B* | *AC*).

Usually *P*(*A* | *C*) is called the prior probability and *P*(*A* | *BC*) the
posterior probability. It should be noted, however, that this
distinction is relative to the observation; the posterior probability
for one observation is the prior probability for the next observation.