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The Addition Rule
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 as follows:
$P(A\cup B)=P(A)+P(B)P(A\cap B).$  The reason for subtracting the last term is that it has already 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$P(A \cup B)=P(A) + P(B).$
Terms

addition rule
The probability that
$A$ or$B$ will happen is the sum of the probabilities that$A$ will happen and that$B$ will happen, minus the probability that both$A$ and$B$ will happen. 
probability
The relative likelihood of an event happening.
Full Text
Addition Law
The addition law of probability (aka addition rule or sum rule), states that the probability that
Example:
Consider the following example. When drawing one card out of a deck of 52 playing cards, what is the probability of getting a face card (king, queen, or jack) or a heart? Let
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
Sources
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Cite This Source
Source: Boundless. “The Addition Rule.” Boundless Statistics. Boundless, 03 Jun. 2016. Retrieved 24 Aug. 2016 from https://www.boundless.com/statistics/textbooks/boundlessstatisticstextbook/probability8/probabilityrules34/theadditionrule1704444/