Chain rule of probability

In the last article, we discussed the concept of conditional probability and we know that the formula for computing the conditional probability is as follows:

We can re-arrange the terms in this formula

Similarly, we have the formula for P(B | A)

Let’s take an example to understand the above formula, say the sample space is represented by omega and represents the population of a country and set A is the set of people who are infected by COVID-19, and set B is the set of people for whom the test results have come out to be positive

In such scenarios, 4 events are of interest to us:

The first one is A intersection B which represents the people who have the COVID-19 symptoms and their test results have come out to be positive and that lies in the intersection region as highlighted in the below image: