1. Lesson #9 Rules of Probability

2. Venn Diagram S A

3. AB P( A or B ) = P( A  B ) P( A and B ) = P( A  B ) S

4. Which diagram shows mutually exclusive events?

6. The complement of event A, denoted by A’ (or ) contains all outcomes not contained in event A. AA’ P(A) + P(A’) = 1 Complement Law: P(A’) = 1 – P(A)

7. AB General Addition Rule: P(A or B) = P(A)+ P(B) - P(A and B)

8. Cats Dogs Female Male 6 4 5 10 11 14 10 15 25 P(Cat) = =.4 P(Dog or Male)= P(D) + P(M) – P(D and M) =.76

9. Conditional Probability: BA

10. Cats Dogs Female Male 6 4 5 10 11 14 10 15 25 P(Female | Cat)

11. Cats Dogs Female Male 6 4 5 10 11 14 10 15 25 P(Female | Cat) =.6

12. LC no LC Smoke No Smoke 12 3 88 147 100 150 P(LC | Smoke) =.12 P(LC | No Smoke) =.02

13. General Multiplication Rule: Recall P(A and B) = P(B)×P(A | B) = P(A)×P(B | A)

14. 10 women and 6 men P(W1 and W2) = P(W1)×P(W2 | W1) W W W W W W W W M M M

15. Independence: If events A and B are independent, P(B | A) = P(B)  P(A and B) = P(A)  P(B) P(Heads on 2 coin flips)= (.5)(.5) =.25 P(Heads on 5 coin flips)= (.5) 5 =.03125