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The Multiplication Rule
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The multiplication rule states that the probability that
Learning Objective

Apply the multiplication rule to calculate the probability of both
$A$ and$B$ occurring
Key Points
 The multiplication rule can be written as:
$P(A \cap B) = P(B) \cdot P(AB)$ .  We obtain the general multiplication rule by multiplying both sides of the definition of conditional probability by the denominator.
Term

sample space
The set of all possible outcomes of a game, experiment or other situation.
Full Text
The Multiplication Rule
In probability theory, the Multiplication Rule states that the probability that
Switching the role of
We obtain the general multiplication rule by multiplying both sides of the definition of conditional probability by the denominator. That is, in the equation
The rule is useful when we know both
Example
Suppose that we draw two cards out of a deck of cards and let
And:
The denominator in the second equation is
Independent Event
Note that when
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Key Term Reference
 conditional probability
 Appears in these related concepts: Conditional Probability, Basic Concepts, and Contingency Tables
 event
 Appears in this related concept: Guidelines for Plotting Frequency Distributions
 experiment
 Appears in these related concepts: Experiments, Primary Market Research, and Descriptive and Correlational Statistics
 independent
 Appears in these related concepts: Fundamentals of Probability, Unions and Intersections, and Party Identification
 multiplication rule
 Appears in these related concepts: The Collins Case, Independence, and Sampling from a small population (special topic)
 probability
 Appears in these related concepts: The Addition Rule, Theoretical Probability, and Rules of Probability for Mendelian Inheritance
 probability theory
 Appears in these related concepts: Applications of Statistics, Complementary Events, and Independence
Sources
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Cite This Source
Source: Boundless. “The Multiplication Rule.” Boundless Statistics Boundless, 14 Oct. 2016. Retrieved 28 Feb. 2017 from https://www.boundless.com/statistics/textbooks/boundlessstatisticstextbook/probability8/probabilityrules34/themultiplicationrule1714445/