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The Multiplication Rule
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.
Terms

sample space
The set of all possible outcomes of a game, experiment or other situation.

multiplication rule
The probability that
$A$ and$B$ occur is equal to the probability that$A$ occurs times the probability that$B$ occurs, given that we know$A$ has already occurred.
Full Text
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
As an example, suppose that we draw two cards out of a deck of cards and let
and
The denominator in the latter equation is 51 since we know a card has been drawn already. Therefore, there are 51 left in total. We also know the first card was an ace, therefore:
Independent Event
Note that when
Assign just this concept or entire chapters to your class for free.
Key Term Reference
 conditional probability
 Appears in these related concepts: Basic Concepts, Contingency Tables, and Conditional Probability
 experiment
 Appears in these related concepts: Experiments, Descriptive and Correlational Statistics, and Primary Market Research
 independent
 Appears in these related concepts: Fundamentals of Probability, Unions and Intersections, and Party Identification
 probability
 Appears in these related concepts: Theoretical Probability, Rules of Probability for Mendelian Inheritance, and The Addition Rule
 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, 08 Aug. 2016. Retrieved 26 Sep. 2016 from https://www.boundless.com/statistics/textbooks/boundlessstatisticstextbook/probability8/probabilityrules34/themultiplicationrule1714445/