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The Addition Rule
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The addition rule states the probability of two events is the sum of the probability that either will happen minus the probability that both will happen.
Learning Objective

Calculate the probability of an event using the addition rule
Key Points
 The addition rule is:
$P(A\cup B)=P(A)+P(B)P(A\cap B).$  The last term has been accounted for twice, once in
$P(A)$ and once in$P(B)$ , so it must be subtracted once so that it is not doublecounted.  If
$A$ and$B$ are disjoint, then$P(A\cap B)=0$ , so the formula becomes$P(A \cup B)=P(A) + P(B).$
Term

probability
The relative likelihood of an event happening.
Full Text
Addition Law
The addition law of probability (sometimes referred to as the addition rule or sum rule), states that the probability that
Consider the following example. When drawing one card out of a deck of
Using the addition rule, we get:
The reason for subtracting the last term is that otherwise we would be counting the middle section twice (since
Addition Rule for Disjoint Events
Suppose
The symbol
Example:
Suppose a card is drawn from a deck of 52 playing cards: what is the probability of getting a king or a queen? Let
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Key Term Reference
 disjoint
 Appears in these related concepts: The Poisson Random Variable, Fundamentals of Probability, and Unions and Intersections
 event
 Appears in these related concepts: Guidelines for Plotting Frequency Distributions, Conditional Probability, and Independence
Sources
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Cite This Source
Source: Boundless. “The Addition Rule.” Boundless Statistics Boundless, 14 Oct. 2016. Retrieved 24 Feb. 2017 from https://www.boundless.com/statistics/textbooks/boundlessstatisticstextbook/probability8/probabilityrules34/theadditionrule1704444/