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**Section 5.2 The Addition Rule and Complements**

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**All disjoint events in a sample space sum to**

KEY IDEA All disjoint events in a sample space sum to 1

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**Two events are disjoint if they have no outcomes in common.**

Disjoint events are also called mutually exclusive events. Example: Toss a coin. H and T are disjoint. Example: Roll a die. 1,2,3,4,5,6 are disjoint. Example: Roll a die. The events E={1,2,3} and F={4,5,6} are disjoint. Example: Roll a die. The events E={1,2,3} and F={2,4,6} are not disjoint. They share {2}.

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**Venn Diagrams Used to display simple probability logic**

Venn Diagrams Used to display simple probability logic. But requires special software to draw on computer.

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**Let S=sample space={1,2,3,4,5,6,7,8,9,10} A={1,2,3,4,10), B={4,5,6,7,9} **

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**“Union of A and B” = A or B = A U B**

= { 1, 2, 3, 4, 5, 6, 7, 9, 10 } “Intersection of A and B” = A and B = A ∩ B = { 4 } “Not A” = complement of A = AC = {5, 6, 7, 8, 9}

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**Addition Rule for Disjoint Events P(A or B) = P(A U B) = P(A) + P(B) IF A and B are disjoint events **

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**For non-disjoint and disjoint events P(A U B) = P(A) + P(B) – P(A∩B)**

Notice 1: P(A)+P(B) counts intersection twice. Notice 2: If A and B are disjoint, P(A∩B)=0.

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**Complement Rule P(AC)=1-P(A)**

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**Show P(A U B) = P(A) + P(B) – P(A∩B)**

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**P(A and C) = ? P(A or C ) = ? P(A and B) = ? P(A or B) = ? P(A or B or C)=? **

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**From a 52 card deck, what is P( Spades or King)?**

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