**Derivation of the Bayes' theorem** can be made by the multiplication rule of probability and some algebra.

[Error: Macro 'mathequation' doesn't exist]

and

[Error: Macro 'mathequation' doesn't exist]

Subtracting these two equations leads:

[Error: Macro 'mathequation' doesn't exist]

and some algebraic transformation

[Error: Macro 'mathequation' doesn't exist]

yields the theorem

[Error: Macro 'mathequation' doesn't exist]