#math #stats 
P(A)P(B|A) = P(B)P(A|B)
If you know P(A|B) and want P(B|A):
#### definition of [[Conditional Expectations|conditional probability]]:
$$P(B|A)=\frac{P(B)P(A|B)}{P(A)}$$
since
$$P(B|A)=\frac{P(B\cap A)}{P(A)}$$
because of [[joint probability]].

[wikipedia](https://en.wikipedia.org/wiki/Bayes%27_theorem)