1. Section 3-3 The Addition Rule

2. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

3. Mutually Exclusive events – two events that cannot happen at the same time What is the probability of rolling a number on a die less than 3 or more than 3? 1212 4 5 6 3

4. Example #1 A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleists, 8 Maxflis, and 3 Top-flites, find the probability… a. A golf ball is a Titleist or Maxfli. b. A golf ball is a Maxfli or Top-Flite. c. A golf ball is not a Top-Flite.

5. Example 2 A standard deck of cards contains 52 cards. One card is randomly selected from the deck. What is the probability.. a. Of randomly selecting a heart or club. b. Of randomly selecting a 5,6, or 7.

6. Not Mutually Exclusive – Two events that can happen at the same time, two events that have something in common What is the probability of rolling a number on a die less than 5 or more than 3? 1 2 4 3 5 6

7. Mutually Exclusive or Not Mutually Exclusive? S = {1,2,3,4,5,6,7,8,9,10,11,12} E = {2,3,4,5,6,7} F = {5,6,7,8,9} G = {9,10,11,12} H = {2,3,4} 1. Are E and F mutually exclusive? 2. Are F and G mutually exclusive? 3. Are E and G mutually exclusive? 4. Are F and H mutually exclusive?

8. Addition Rule – “or” The probability that A or B. One event Not Mutually Exclusive: P(A or B) = P(A) + P(B) – P(A and B)

9. Randomly select an individual who is either male or wearing black  NOT mutually exclusive because some (2) of the males are black …

10. Find the probability of randomly selecting a female or seated.

11. Find the probability of randomly selecting a female or wearing black.

12. Roll a Die … Find the probability of rolling an even number or a number greater than 3.

13. Find the probability of randomly selecting one person from the Titanic roster, and that person being a man or a boy.

14. Find the probability of randomly selecting one person from the Titanic roster, and that person being a man or survived.

15. Find the probability of randomly selecting one person from the Titanic roster, and that person being a woman or survived.

16. Ticket Issued No Ticket Issued Total Speeding40170210 No Taillights103545 No Signal52530 Careless Driving4570115 Total100300400 1.What is the probability that a ticket was issued? 2.What’s the probability a car did not have taillights? 3.What’s the probability a driver will get a ticket, given that they were stopped for careless driving? 4.What the probability a person was stopped for speeding or failure to use signals?

17. Mixed Practice Ticket Issued No Ticket Issued Total Speeding40170210 No Taillights103545 No Signal52530 Careless Driving4570115 Total100300400 5. Given a ticket was not issued, what’s the probability a person was stopped for speeding? 6. What’s the probability that the first person got a speeding ticket and the second person got a ticket for no signal?

18. Homework: HW p 136, #15 - 20 Quiz tomorrow on conditional probability