2. Copyright © 2011 Pearson Education, Inc. Probability: Living with the Odds Discussion Paragraph 7A 1 web 70. Blood Groups 71. Accidents 1 world 72. Probability in the News 73. Probability in your Life 74. Gambling Odds

3. Copyright © 2011 Pearson Education, Inc. Slide 7-3 Unit 7B Combining Probabilities

4. 7-B Copyright © 2011 Pearson Education, Inc. Slide 7-4 Two events are independent if the outcome of one does not affect the probability of the other event. If two independent events A and B have individual probabilities P(A) and P(B), the probability that A and B occur together is P(A and B) = P(A) P(B). This principle can be extended to any number of independent events. And Probability: Independent Events

5. 7-B Consecutive Floods CN (1) 1. Find the probability that a 100-year flood (a flood with a.01 probability of striking in a given year) will strike a city in two consecutive years. Assume that ta flood in one year does not affect the likelihood of a flood in the next year. Copyright © 2011 Pearson Education, Inc. Slide 7-5

6. 7-B Three Coins CN (2) Suppose you toss three coins. 2. What is the probability of getting three tails? Copyright © 2011 Pearson Education, Inc. Slide 7-6

7. 7-B Copyright © 2011 Pearson Education, Inc. Slide 7-7 Two events are dependent if the outcome of one affects the probability of the other event. The probability that dependent events A and B occur together is P(A and B) = P(A) P(B given A) where P(B given A) is the probability of event B given the occurrence of event A. This principle can be extended to any number of dependent events. And Probability: Dependent Events

8. 7-B Bingo CN (3) The game of Bingo involves drawing labeled buttons from a bin at random, without replacement. There are 75 buttons, 15 for each of the letters B, I, N, B, and O. 3. What is the probability of drawing two B buttons in the first two selections? Copyright © 2011 Pearson Education, Inc. Slide 7-8

9. 7-B Jury Selection CN (4) A three-person jury must be selected at random from a pool of 12 people that has 6 men and 6 women. 4. What is the probability of selecting an all-male jury? Copyright © 2011 Pearson Education, Inc. Slide 7-9

10. 7-B Copyright © 2011 Pearson Education, Inc. Slide 7-10 Two events are non- overlapping if they cannot occur together, like the outcome of a coin toss, as shown to the right. For non-overlapping events A and B, the probability that either A or B occurs is shown below. P(A or B) = P(A) + P(B) This principle can be extended to any number of non-overlapping events. Either/Or Probabilities: Non-Overlapping Events

11. 7-B Either/Or Dice CN (5) Suppose you roll a single die. 5. What is the probability of rolling either a 2 or a 3? Copyright © 2011 Pearson Education, Inc. Slide 7-11

12. 7-B Copyright © 2011 Pearson Education, Inc. Slide 7-12 Two events are overlapping if they can occur together, like the outcome of picking a queen or a club, as shown to the right. For overlapping events A and B, the probability that either A or B occurs is shown below. P(A or B) = P(A) + P(B) – P(A and B) This principle can be extended to any number of overlapping events. Either/Or Probabilities: Overlapping Events

13. 7-B Democrats and Women CN (6) You select one person at random from a room with eight people: two Democratic men, two Republican men, two Democratic women, and two Republican women. 6. What is the probability that you will select either a woman or a Democrat? Copyright © 2011 Pearson Education, Inc. Slide 7-13

14. 7-B Copyright © 2011 Pearson Education, Inc. Slide 7-14 What is the probability of rolling either a 3 or a 4 on a single six-sided die? These are non-overlapping events. P(A or B) = P(A) + P(B) P(3 or 4) = P(3) + P(4) = 1/6 + 1/6 = 2/6 = 1/3 What is the probability that in a standard shuffled deck of cards you will draw a 5 or a spade? These are overlapping events. P(A or B) = P(A) + P(B) – P(A and B) P(5 or spade) = P(5) + P(spade) – P(5 and spade) = 4/52 + 13/52 – 1/52 = 16/52 = 4/13 Examples

15. 7-B Copyright © 2011 Pearson Education, Inc. Slide 7-15 The At Least Once Rule (For Independent Events) Suppose the probability of an event A occurring in one trial is P(A). If all trials are independent, the probability that event A occurs at least once in n trials is shown below. P(at least one event A in n trials) = 1 – P(not event A in n trials) = 1 – [P(not A in one trial)] n

16. 7-B 100 Year Flood CN (7) 7. What is the probability that a region will experience at least one 100-year flood (a flood that has a.01 chance of occurring in any given year) during the next 100 years? Assume that 100-year floods in consecutive years are independent events. Copyright © 2011 Pearson Education, Inc. Slide 7-16

17. 7-B Lottery Chances CN (8) You purchase 10 lottery tickets, for which the probability of winning some prize on a single ticket is 1 in 10. 8. What is the probability that you will have at least one winning ticket among the 10 tickets? Copyright © 2011 Pearson Education, Inc. Slide 7-17

18. 7-B Quick Quiz CN (9) 9. Please answer the 10 quick quiz multiple choice questions on p. 435. Copyright © 2011 Pearson Education, Inc. Slide 7-18

19. 7-B Homework 7B Discussion Paragraph 7A Class Notes 1-9 p. 436: 1-10 1 web 59. Lottery Chances 60. HIV Probabilities 1 world 61. Combined Probability in the News 62. Combined Probability in Your Life Copyright © 2011 Pearson Education, Inc. Slide 7-19