Bayes' theorem

Bayes’ theorem is given by:

$$P(Y=k|X=x)=\frac{{\pi }_k{f}_k(x)}{{\sum }_{l=1}^K{\pi }_l{f}_l(x)}$$

For multiple events:

$$P(B_i|A)=\frac{P(B_i)P(A|B_i)}{{\sum }_{k=0}^{n}P(B_k)P(A|B_k)}$$