In this section, we will state and prove both Bayes' theorem and its extension.
Bayes' theorem and its extension
Bayes' theorem
Bayes' theorem states the following:
Proof
We can prove this theorem by using elementary set theory on the probability spaces of the events A and B. In other words, here, a probability event will be defined as a set of the possible outcomes in the probability space:
Figure 2.1: Probability space for the two events
As you can see in the preceding diagram, we can state the following relationships:
Rearranging these relationships...
