1. © 2002 Thomson / South-Western Slide 4B-1 Chapter 4, Part B Probability

2. © 2002 Thomson / South-Western Slide 4B-2 Four Types of Probability Marginal Probability Union Probability Joint Probability Conditional Probability

3. © 2002 Thomson / South-Western Slide 4B-3 Four Types of Probability Marginal The probability of X occurring Union The probability of X or Y occurring Joint The probability of X and Y occurring Conditional The probability of X occurring given that Y has occurred Y X Y X Y X

4. © 2002 Thomson / South-Western Slide 4B-4 General Law of Addition Y X

5. © 2002 Thomson / South-Western Slide 4B-5 General Law of Addition -- Example S N.56.67.70

6. © 2002 Thomson / South-Western Slide 4B-6 Office Design Problem Probability Matrix.11.19.30.56.14.70.67.331.00 Increase Storage Space YesNoTotal Yes No Total Noise Reduction

7. © 2002 Thomson / South-Western Slide 4B-7 Office Design Problem Probability Matrix, continued (2).11.19.30.56.14.70.67.331.00 Increase Storage Space YesNoTotal Yes No Total Noise Reduction

8. © 2002 Thomson / South-Western Slide 4B-8 Office Design Problem Probability Matrix, continued (3).11.19.30.56.14.70.67.331.00 Increase Storage Space YesNoTotal Yes No Total Noise Reduction

9. © 2002 Thomson / South-Western Slide 4B-9 Venn Diagram of the X or Y but Not Both Case Y X

10. © 2002 Thomson / South-Western Slide 4B-10 Complement of a Union: The Neither/Nor Region Y X

11. © 2002 Thomson / South-Western Slide 4B-11 Office Design Problem: The Neither/Nor Region S N

12. © 2002 Thomson / South-Western Slide 4B-12 Special Law of Addition X Y

13. © 2002 Thomson / South-Western Slide 4B-13 Demonstration Problem 4.3 Type ofGender PositionMaleFemaleTotal Managerial8311 Professional311344 Technical521769 Clerical92231 Total10055155

14. © 2002 Thomson / South-Western Slide 4B-14 Demonstration Problem 4.3, continued Type ofGender PositionMaleFemaleTotal Managerial8311 Professional311344 Technical521769 Clerical92231 Total10055155

15. © 2002 Thomson / South-Western Slide 4B-15 Law of Multiplication and Demonstration Problem 4.5

16. © 2002 Thomson / South-Western Slide 4B-16 Special Law of Multiplication for Independent Events General Law Special Law

17. © 2002 Thomson / South-Western Slide 4B-17 Law of Conditional Probability The conditional probability of X given Y is the joint probability of X and Y divided by the marginal probability of Y.

18. © 2002 Thomson / South-Western Slide 4B-18 Law of Conditional Probability and the Office Design Problem N S.56.70

19. © 2002 Thomson / South-Western Slide 4B-19 Office Design Problem, continued.19.30.14.70.331.00 Increase Storage Space YesNoTotal Yes No Total Noise Reduction.11.56.67

20. © 2002 Thomson / South-Western Slide 4B-20 Independent Events If X and Y are independent events, the occurrence of Y does not affect the probability of X occurring. If X and Y are independent events, the occurrence of X does not affect the probability of Y occurring.

21. © 2002 Thomson / South-Western Slide 4B-21 Revision of Probabilities: Bayes’ Rule Bayes’ Rule is an extension to the conditional law of probabilities Enables revision of original probabilities with new information

22. © 2002 Thomson / South-Western Slide 4B-22 Revision of Probabilities with Bayes' Rule: Ribbon Problem

23. © 2002 Thomson / South-Western Slide 4B-23 Revision of Probabilities with Bayes’ Rule: Ribbon Problem Conditional Probability 0.052 0.042 0.094 0.65 0.35 0.08 0.12 0.052 0.094 =0.553 0.042 0.094 =0.447 Alamo South Jersey Event Prior Probability Joint Probability PEd i ()  Revised Probability PEd i (|) PdE i (|)

24. © 2002 Thomson / South-Western Slide 4B-24 Revision of Probabilities with Bayes' Rule: Ribbon Problem Alamo 0.65 South Jersey 0.35 Defective 0.08 Defective 0.12 Acceptable 0.92 Acceptable 0.88 0.052 0.042 + 0.094