The Multiplication Rule of Probability | Probability of Complex Events
Probability Theory Basics

# 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?

Section 2. Chapter 3

Course Content

Probability Theory Basics

# 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?

Section 2. Chapter 3