Lessons

- 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

# Dependent Vs. Independent Events in Probability

Two events are said to be independent if the occurrence of one event is in no way affected by the occurrence of the other event. Suppose we roll a die and receive a 6. The second time we roll the die, its outcome will not be affected by the fact that we received a 6 in the first roll. The outcome of each roll is independent of each other.

To be independent, one of the following conditions must be true:

**P(A | B) = P(A) or P(B | A) = P(B)**

If the two events are not independent, then they are said to be dependent, that is, the occurrence of one event influences the occurrence of another event.