Multiplication, Addition and Total Probability Rules
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 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