Multiplication, Addition and Total Probability Rules

Addition Rule

The additional rule determines the probability of atleast one of the events occuring.

rule1
rule1

If A and B are mutually exclusive, then P(A and B) = 0, so the rule can be simplified as follows:

rule2
rule2

Multiplication Rule

Multiplication rule determines the joint probability of two events.

rule3
rule3

Joint probability of A and B is equal to the probability of A given B multiplied by the probability of B.

If A and B are independent, then P (A/B) = P (A)and the multiplication rule simplifies to:

rule4
rule4

Total Probability Rule

The total probability rule determines the unconditional probability of an event in terms of probabilities conditional on scenarios.

rule5
rule5

Let’s take an example to understand this.

Event A: Company X’s stock price will rise.

Event B: Inflation will fall. P(B) = 0.6. Therefore, probability of inflation not falling, P(BC) = 0.4

Probability of stock price rising given a fall in inflation, P(A|B) = 0.8

Probability of stock price rising given no fall in inflation, P(A|BC) = 0.6

We can use the total probability rule to calculate the probability of a rise in stock price as follows:

rule6
rule6

This is the total probability of event A occuring under all scenarios.