1. Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 2 - Slide 1 P-2 Probability Theoretical Probability

2. Chapter 12 Section 2 - Slide 2 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Theoretical probability

3. Chapter 12 Section 2 - Slide 3 Copyright © 2009 Pearson Education, Inc. Equally likely outcomes If each outcome of an experiment has the same chance of occurring as any other outcome, they are said to be equally likely outcomes. For equally likely outcomes, the probability of Event E may be calculated with the following formula.

4. Chapter 12 Section 2 - Slide 4 Copyright © 2009 Pearson Education, Inc. Example A six-sided die is rolled. Find the probability of rolling a) a 2. b) an odd number. c) a number less than 4. d) an 8. e) a number less than 9.

5. Chapter 12 Section 2 - Slide 5 Copyright © 2009 Pearson Education, Inc. Solutions: There are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. a) b) There are three ways an odd number can occur: 1, 3 or 5. c) Three numbers are less than 4.

6. Chapter 12 Section 2 - Slide 6 Copyright © 2009 Pearson Education, Inc. d) There are no outcomes that will result in an 8. e) All outcomes are less than 9. The event must occur and the probability is 1. Solutions: There are six equally likely outcomes: 1, 2, 3, 4, 5, and 6 (continued)

7. Chapter 12 Section 2 - Slide 7 Copyright © 2009 Pearson Education, Inc. Important Facts The probability of an event that cannot occur is 0. The probability of an event that must occur is 1. Every probability is a number between 0 and 1 inclusive; that is, 0  P(E)  1. The sum of the probabilities of all possible outcomes of an experiment is 1.

8. Chapter 12 Section 2 - Slide 8 Copyright © 2009 Pearson Education, Inc. Example A standard deck of cards is well shuffled. Find the probability that the card is selected. a) a 10. b) not a 10. c) a heart. d) an ace, 2, or 3. e) diamond and spade. f) a card greater than 4 and less than 7.

9. Chapter 12 Section 2 - Slide 9 Copyright © 2009 Pearson Education, Inc. Example (continued) a) a 10 There are four 10’s in a deck of 52 cards. b) not a 10

10. Chapter 12 Section 2 - Slide 10 Copyright © 2009 Pearson Education, Inc. Example continued c) a heart There are 13 hearts in the deck. d) an ace, 2 or 3 There are 4 aces, 4 twos and 4 threes, or a total of 12 cards.

11. Chapter 12 Section 2 - Slide 11 Copyright © 2009 Pearson Education, Inc. Example continued d) diamond and spade The word and means both events must occur. This is not possible. e) a card greater than 4 and less than 7 The cards greater than 4 and less than 7 are 5’s and 6’s (or a total of 8 cards).

12. Slide 12 - 12 Copyright © 2009 Pearson Education, Inc. Each of the numbers 0-9 is written on a sheet of paper and the ten sheets of paper are placed in a box. If one sheet of paper is selected at random from the box, determine the probability that the number selected is odd. a. c. b. d.

13. Slide 12 - 13 Copyright © 2009 Pearson Education, Inc. Each of the numbers 0-9 is written on a sheet of paper and the ten sheets of paper are placed in a box. If one sheet of paper is selected at random from the box, determine the probability that the number selected is odd. a. c. b. d.

14. Slide 12 - 14 Copyright © 2009 Pearson Education, Inc. Each of the numbers 0-9 is written on a sheet of paper and the ten sheets of paper are placed in a box. If one sheet of paper is selected at random from the box, determine the probability that the number selected is less than 3. a. c. b. d.

15. Slide 12 - 15 Copyright © 2009 Pearson Education, Inc. Each of the numbers 0-9 is written on a sheet of paper and the ten sheets of paper are placed in a box. If one sheet of paper is selected at random from the box, determine the probability that the number selected is less than 3. a. c. b. d.

16. Slide 12 - 16 Copyright © 2009 Pearson Education, Inc. Yesterday’s Experiment/Data

17. Slide 12 - 17 Copyright © 2009 Pearson Education, Inc. Practice Problems

18. Slide 12 - 18 Copyright © 2009 Pearson Education, Inc. Practice Problems

19. Slide 12 - 19 Copyright © 2009 Pearson Education, Inc. Practice Problems

20. Slide 12 - 20 Copyright © 2009 Pearson Education, Inc.

21. Slide 12 - 21 Copyright © 2009 Pearson Education, Inc.