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3.3 Finding Probability Using Sets

3.3 Finding Probability Using Sets. Set Theory Definitions. Simple event Has one outcome E.g. rolling a die and getting a 4 or pulling one name out of a hat Compound event Consists of 2 or more simple events E.g. rolling a die and getting a 2 and an even number. Set Theory Definitions.

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3.3 Finding Probability Using Sets

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  1. 3.3 Finding Probability Using Sets

  2. Set Theory Definitions • Simple event • Has one outcome • E.g. rolling a die and getting a 4 or pulling one name out of a hat • Compound event • Consists of 2 or more simple events • E.g. rolling a die and getting a 2 and an even number

  3. Set Theory Definitions • Venn Diagram • Used to illustrate relationships between sets of items • Especially when the sets have some items in common • Subset • A set whose members are all members of another set • A is a subset of S, A  S

  4. S B A Intersection of Sets • Given two sets A and B, the set of common elements of A and B • We say “A and B” • We write A  B

  5. S B A Disjoint Sets • Sets that have no elements in common • Intersection is the empty set, represented by  • Also called the null set • A  B =  • n(A  B) = 0 • we say events A and B are mutually exclusive • ′ = S • S′ = 

  6. S B A Union of Sets • A set consisting of all the elements of A as well as B • We say “A or B” • Represented by A  B

  7. S B A Principle of Inclusion and Exclusion n(A  B) = n(A) + n(B) – n(A  B) Why? A  B has been shaded twice If A and B are disjoint n(A  B) = n(A) + n(B)

  8. Additive Principle: Probability of Union of Two Events P(A  B) = P(A) + P(B) – P(A  B) If A and B are mutually exclusive events P(A  B) = P(A) + P(B)

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