1. CONDITIONAL PROBABILITY 3.2 Raise your hand when you are finished reading.

2. The probability of an event occurring, given that another event has already occurred. The conditional probability of event B occurring, given that event A has occurred, is denoted by P(B/A) Conditional Probability

3. STARTING SIMPLE There are more red coins among the large coins than among the small coins. When randomly selecting a coin from the box, the probability of obtaining a red coin is what? P(red) = 5/10 = 1/2 because there are 5 red coins in a total of 10 coins.

4. NOW ASSUME THAT A COIN IS PICKED BY A BLINDFOLDED PERSON. The coin can be felt to be large, but the color is unknown. What is the probability that the coin is red and large?

5. IN THIS CASE P(RED AND LARGE) = 3/5 Because all the small coins are ruled out and only the large coins are considered. There are 5 large coins, 3 of which happen to be red.

6. DEPENDENT

7. INDEPENDENT Two events are independent when the occurrence of one of the events does not affect the probability of the occurrence of the other event. Two events A and B are independent when P(B/A)=P(B) or when P(A/B)=P(A)

8. INDEPENDENT P(B/A)=P(B) or when P(A/B)=P(A) “the probability of B, given A” A is the event that happened first B is the event that is happening second Because they are independent The first event does not affect the Probability of the second event.

9. ROLL THE DICE Roll the first Dice then roll the second dice 1.) What is the probability that you will roll the same number again? 2.) What is the probability that you will roll an even number?

10. DEPENDENT OR INDEPENDENT 1.) Returning a movie after the due date and receiving a late fee. 2.) A father having hazel eyes and a daughter having hazel eyes. 3.) Select a 10 from a deck of cards, replacing it, and then selecting a 10 from the deck again.

11. THE MULTIPLICATION RULE

12. USING THE MULTIPLICATION RULE

13. USING MULTIPLICATION RULE To Find Probabilities For anterior cruciate ligament (ACL) reconstructive surgery, the probability that the surgery is successful is 0.95. Find the probability that three ACL surgeries are successful.

14. EXAMPLE 1

15. EXAMPLE 2 To Find Probabilities For anterior cruciate ligament (ACL) reconstructive surgery, the probability that the surgery is successful is 0.95. 2.) Find the probability that none of the three ACL surgeries are successful.

16. EXAMPLE 2 CONTINUED

17. EXAMPLE 3 For anterior cruciate ligament (ACL) reconstructive surgery, the probability that the surgery is successful is 0.95. 3.) Find the probability that at least one of the three ACL surgeries is successful.

18. EXAMPLE 3 CONTINUED

19. USING THE MULTIPLICATION RULE

20. QUESTION 1

21. QUESTION 2

22. QUESTION 3

23. TRY http://www.regentsprep.org/regents/math/algebra/ APR3/PracCond.htm #’s 1 and 2