1. Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 1 - Slide 1 P-1 Probability The Nature of Probability

2. Chapter 12 Section 1 - Slide 2 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Empirical probability and theoretical probability Law of Large Numbers

3. Chapter 12 Section 1 - Slide 3 Copyright © 2009 Pearson Education, Inc. Definitions An experiment is a controlled operation that yields a set of results. The possible results of an experiment are called its outcomes. An event is a subcollection of the outcomes of an experiment.

4. Chapter 12 Section 1 - Slide 4 Copyright © 2009 Pearson Education, Inc. Definitions (continued) Empirical probability is the relative frequency of occurrence of an event and is determined by actual observations of an experiment. Theoretical probability is determined through a study of the possible outcomes that can occur for the given experiment.

5. Chapter 12 Section 1 - Slide 5 Copyright © 2009 Pearson Education, Inc. Empirical Probability Example: In 100 tosses of a fair die, 19 landed showing a 3. Find the empirical probability of the die landing showing a 3. Let E be the event of the die landing showing a 3.

6. Chapter 12 Section 1 - Slide 6 Copyright © 2009 Pearson Education, Inc. The Law of Large Numbers The law of large numbers states that probability statements apply in practice to a large number of trials, not to a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals.

7. Slide 12 - 7 Copyright © 2009 Pearson Education, Inc. Of 12 children playing at the playground, 4 are playing on the swing set. Determine the empirical probability that the next child to the playground will play on the swing set. a. c. b. d.

8. Slide 12 - 8 Copyright © 2009 Pearson Education, Inc. Of 12 children playing at the playground, 4 are playing on the swing set. Determine the empirical probability that the next child to the playground will play on the swing set. a. c. b. d.

9. Slide 12 - 9 Copyright © 2009 Pearson Education, Inc. Empirical Probability Experiment Take 3 dice Roll 1 die 25+ times & record results Roll 2 dice 25+ times & record results Roll 3 dice 25+ times and record results

10. Slide 12 - 10 Copyright © 2009 Pearson Education, Inc. Empirical Probability Experiment Create and complete 3 frequency tables as shown: 1’s2’s3’s4’s5’s6’s 2’s3’s4’s5’s6’s7’s8’s9’s10’s11’s12’s 3’s4’s5’s6’s7’s8’s9’s10’s11’s12’s13’s14’s15’s16’s17’s18’s

11. Slide 12 - 11 Copyright © 2009 Pearson Education, Inc.