# Multiplication, Addition and Total Probability Rules

### Addition Rule

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

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

### Multiplication Rule

Multiplication rule determines the joint probability of two events.

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:

### Total Probability Rule

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

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:

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

- Probability - Basic Terminology
- Two Defining Properties of Probability
- Empirical, Subjective and Priori Probability
- State the Probability of an Event as Odds
- Unconditional and Conditional Probabilities
- Multiplication, Addition and Total Probability Rules
- Joint Probability of Two Events
- Probability of Atleast One of the Events Occuring
- Dependent Vs. Independent Events in Probability
- Joint Probability of a Number of Independent Events
- Unconditional Probability Using Total Probability Rule
- Expected Value of Investments
- Calculating Variance and Standard Deviation of Stock Returns
- Conditional Expected Values
- Calculating Covariance and Correlation
- Expected Value of a Portfolio
- Variance and Standard Deviation of a Portfolio
- Bayes’ Theorem
- Multiplication Rule of Counting
- Permutation and Combination Formula

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