1. Chapter 12 Probability © 2008 Pearson Addison-Wesley. All rights reserved

2. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-2 Chapter 12: Probability 12.1 Basic Concepts 12.2 Events Involving “Not” and “Or” 12.3 Conditional Probability; Events Involving “And” 12.4 Binomial Probability 12.5Expected Value

3. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-3 Chapter 1 Section 12-2 Events Involving “Not” and “Or”

4. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-4 Events Involving “Not” and “Or” Properties of Probability Events Involving “Not” Events Involving “Or”

5. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-5 Properties of Probability Let E be an event from the sample space S. That is, E is a subset of S. Then the following properties hold. (The probability of an event is between 0 and 1, inclusive.) (The probability of an impossible event is 0.) (The probability of a certain event is 1.)

6. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-6 Example: Rolling a Die When a single fair die is rolled, find the probability of each event. a) the number 3 is rolled b) a number other than 3 is rolled c) the number 7 is rolled d) a number less than 7 is rolled

7. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-7 Example: Rolling a Die Solution The outcome for the die has six possibilities: {1, 2, 3, 4, 5, 6}.

8. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-8 Events Involving “Not” The table on the next slide shows the correspondences that are the basis for the probability rules developed in this section. For example, the probability of an event not happening involves the complement and subtraction.

9. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-9 Correspondences Set TheoryLogicArithmetic Operation or Connective (Symbol) ComplementNotSubtraction Operation or Connective (Symbol) UnionOrAddition Operation or Connective (Symbol) IntersectionAndMultiplication

10. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-10 Probability of a Complement The probability that an event E will not occur is equal to one minus the probability that it will occur. S So we have E and

11. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-11 Example: Complement When a single card is drawn from a standard 52- card deck, what is the probability that is will not be an ace? Solution

12. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-12 Events Involving “Or” Probability of one event or another should involve the union and addition.

13. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-13 Mutually Exclusive Events Two events A and B are mutually exclusive events if they have no outcomes in common. (Mutually exclusive events cannot occur simultaneously.)

14. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-14 Addition Rule of Probability (for A or B) If A and B are any two events, then If A and B are mutually exclusive, then

15. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-15 Example: Probability Involving “Or” When a single card is drawn from a standard 52- card deck, what is the probability that it will be a king or a diamond? Solution

16. © 2008 Pearson Addison-Wesley. All rights reserved 12-2-16 Example: Probability Involving “Or” If a single die is rolled, what is the probability of a 2 or odd? Solution These are mutually exclusive events.