Just a tidbit for remembering bayes rule:
P(A|B)P(B) = P(A,B) = P(B|A)P(A)
The familiar forms
P(A|B) = P(A,B)/P(B) = P(B|A)P(A)/P(B)
immediately follow
P(A|B)P(B) = P(A,B) = P(B|A)P(A)
The familiar forms
P(A|B) = P(A,B)/P(B) = P(B|A)P(A)/P(B)
immediately follow
https://en.m.wikipedia.org/wiki/Joint_probability_distributi...