Multiplication Rules for Probability

1. Chapter 4 – Probability and Counting Rulessection 4.3 – Multiplication Rules and Conditional Probability

2. Multiplication Rules for Probability Independent Events Two events are independent if the fact that A occurs does not affect the probability of B occuring. • Flip a coin 5 times… • drawing a card, replacing it, drawing again

3. Multiplication Rules for Probability Multiplication Rule 1 When two events are independent, the probability of both occuring is P(A and B) = P(A)P(B) • A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on the die. • A card is drawn and replaced. Find the probability of drawing a queen and then an ace. • The multiplication rule can be extended to many events…

4. Multiplication Rules for Probability Multiplication Rule 2 when two events are dependent, the probability of both occurring is P(A and B) = P(A)·P(B|A) • P(B|A) is a conditional probability • It means the probability that B occurs given that A has already occurred.

5. Multiplication Rules for Probability examples • A person owns 30 CD’s. 5 of them are jazz. If 2 CD’s are selected at random, what is the probability that both are jazz music? • Are the two selections independent? • P(J1and J2) = • 53% of residents of a city have homeowner’s insurance. Of these 27% also have car insurance. Find P(home ins. and car ins.).

6. Multiplication Rules for Probability • try p 220 # 1 in your notes

7. Multiplication Rules for Probability Conditional Probability

8. Multiplication Rules for Probability turn to page 221 • try number 11 in your notes • try number 13

9. Practice • In class • p 220 (2-30 even)