# TOTAL PROBABILITY THEOREM

**TOTAL PROBABILITY THEOREM**

Let E1, E2, ..., En be n mutually exclusive and exhaustive events and event A is such that it can occur with any of the events E1, E2, E3, ....... En then the probability of the occurrence of event A can be

**Example:**

In a certain city only 2 newspapers A and B are published. It is known that 25% of the city population reads A and 20% reads B while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisement and 40% of those who read B but not A look into advertisements while 50% of those who read both A and B look into advertisements. What is the percentage of the population who read an advertisement?

**Solution :**