1. Get out your ISN! You will be able to find P(A and B) for independent and dependent events. Today’s Objectives:

2. 33-34 Multiplication Rule of Independent Events—Two events A and B are independent if the fact that A occurs does not change the probability of B occurring. Dependent Events—When the outcome of the first event changes the probability of the second event occurring. Conditional Probability—The probability that event B occurs knowing that event A already occurred; P(B|A) TOC WWK Probability

3. Big Picture

4. Foldable OUTSIDE INSIDE Fold it in half Cut along the dotted line to form the tabs.

5. Dependent & Independent Events

6. Dependent Independent Dependent

7. Dependent & Independent Events Dependent OR Independent? You accidently dropped a coin from the top of 10 stairs. What is the probability that it will land on the eighth step, tails up?. What is your first event? ________________________________________. Second? ________________________________________. If the coin does land on the eighth step, does that change the probability that it will land tails up? ______________________________ ANSWER: ________________________ Landing on the 8 th step Tails up no Independent

8. Extra Practice There are 3 black cats and 5 grey cats in a cage, and none of them want to be in there. The cage door opens briefly and two cats escape. What is the probability that both escaped cats are black? Event A = Event B = THINK: If the first cat to escape is a black cat, does that change the probability that the second will be a black cat? Black Cat INDEPENDENT? DEPENDENT?

9. Conditional Probability probability of B given A

10. Conditional Probability JackAce JackAce I drew a Jack and now I want to draw an Ace. How many Aces and cards are left in the deck?

11. Conditional Probability 7 >4 7 I drew a 7 and now I want to draw a number >4. How many numbers >4 and total numbers are left in the hat?

12. Multiplication Rule of Probability P(A and B) P(A)*P(B) P(A)*P(B | A) Multiplication Rule of Probability

13. P(A and B) spade

14. P(A and B) AnnieJustin YES, Dependent

15. P(A and B)

17. 34 11/24 Right Side Input Multiplication Rule of Probability Tape Here

18. 33 11/24 Left Side Input Multiplication Rule of Probability Tape Here

19. Homework LEFT side