Bayes’ Rule

Lesson 7 Chapter 2

In order to explain the *Bayes' rule*, let's start with something simple as a **special case**. Assume we have **two events** and . Do you agree with the following statement?

Now, let's calculate the probability of event :

Above, we used the conditional probability rules to expand the event intersections. The above equation asserts that *the probability of event is a weighted average of the conditional probability of given that has occurred and the conditional probability of given that has not happened*. This is a very useful formula as a lot of times, directly calculating the probability of an event such as may not be easy or even possible. This rule conditions the likelihood of an event on different events.

The special case of above, can be extended to the below more general rule called the Bayes' rule.