Probability of A happening as well as B = (Conditional Probability
of A given B) X (Probability of B happening):
P(A,B)=P(A|B)P(B)
This is called Bayes Theorem.
As P(A,B)=P(B,A), we also have P(A,B)=P(B,A)=P(B|A)P(A)
Combining these two we find:
P(A|B)P(B)=P(B|A)P(A)
This is another form of Bayes Theorem. |