Probability

Bayes’ Theorem

Keywords:

PBi|A=PA|Bi·PBiPA

or

PBi|A=PA|Bi·PBii=1nPA|Bi·PBi

or

PBi|A=PA|Bi·PBiPA|B1·PB1+PA|B2·PB2+...+PA|Bn·PBn

where

i=1nBi=B1+B2+...+Bn=Ω

is a complete system of events.

In case i=1

PB|A=PA|B·PBPA ; i=1, B1=B