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. 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 S A B

5. S 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 A B –we say events A and B are mutually exclusive  ′ = S S ′ = 

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

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