Module 1: Basics Concepts of Probability

The key points from this module are:

Probability

The Probability of an event is defined as its long-run relative frequency.

Rules of Probability

There are three main rules associated with basic probability: the addition rule, the multiplication rule, and the complement rule.

Sample Space

Sample Space is the set of all possible outcomes that can happen for a given situation or a chance situation.

Independent Events

Two events are independent if the occurrence of one has no effect on the chance of occurrence of another.

Boole’s Inequality

The probability of the union is less than the sum of the probabilities.

Conditional Probability

Conditional Probability is a measure of the probability of an event occurring, given that another event.

The formula for Conditional Probability is derived from the probability multiplication rule, P(A and B) = P(A)*P(B|A). The probability of A given B is equal to the probability of A and B divided by the probability of B.

Multiplication Rule

The Multiplication Rule is a way to find the probability of two events happening at the same time. A Joint Probability is the probability of intersection, whereas the Marginal Probability is the probability of observing an outcome with a single attribute regardless of other attributes.

Random Variables

Random Variables describe the probability of an uncertain future, the numerical outcome of a random process.