# The Multiplication Rule of Probability

We have already considered that if events A and B are independent, then:`P(A and B) = P(A) *P(B)`

.

This formula is a special case of the more general **probabilities multiplication rule**:

It states that the probability of the joint occurrence of two events, A and B, is equal to the probability of event A multiplied by event B's conditional probability, given that event A has occurred.

## Example

Assume you draw two cards from a standard deck (52 cards) without replacement. What is the probability of drawing a heart on the first card and a diamond on the second?

Event A - drawing a heart first.
Event B - drawing a diamond second.

Note

Pay attention that in the multiplication probabilities rule, the order in which events occur is unimportant - we can consider both the probability

`P(B)*P(A|B)`

and`P(A)*P(B|A)`

.

Everything was clear?

Course Content

Probability Theory Basics

## Probability Theory Basics

5. Covariance and Correlation

# The Multiplication Rule of Probability

We have already considered that if events A and B are independent, then:`P(A and B) = P(A) *P(B)`

.

This formula is a special case of the more general **probabilities multiplication rule**:

It states that the probability of the joint occurrence of two events, A and B, is equal to the probability of event A multiplied by event B's conditional probability, given that event A has occurred.

## Example

Assume you draw two cards from a standard deck (52 cards) without replacement. What is the probability of drawing a heart on the first card and a diamond on the second?

Event A - drawing a heart first.
Event B - drawing a diamond second.

Note

Pay attention that in the multiplication probabilities rule, the order in which events occur is unimportant - we can consider both the probability

`P(B)*P(A|B)`

and`P(A)*P(B|A)`

.

Everything was clear?