Section 5.2 The Addition Rule and Complements

1. Section 5.2The Addition Rule and Complements

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

3. 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}.

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

5. 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}

6. “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}

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

9. 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.

10. Complement Rule P(AC)=1-P(A)

11. Show P(A U B) = P(A) + P(B) – P(A∩B)

12. P(A and C) = ? P(A or C ) = ? P(A and B) = ? P(A or B) = ? P(A or B or C)=?

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