Baye’s theorem provides the best way to represent how probabilities can be reasoned. It allows to use a supplied conditional probability in both directions. It’s a simple mathematical fact given as follows. For two mutually dependent events A and B,

P(B|A) = P(A|B)P(B)/P(A)

The product rule. It can actually be written in two forms:

P(a ∧b) = P(a | b)P(b) and P(a ∧b) = P(b | a)P(a) .

Equating the two right-hand sides and dividing by P(a), we get

P(b | a) =

P(a | b)P(b)

P(a)

This equation is known as Bayes’ rule (also Bayes’ law or Bayes’ theorem). This simple equation underlies most modern AI systems for probabilistic inference