1. Chapter 12 Section 5 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND

2. Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 5 - Slide 2 Chapter 12 Probability

3. Chapter 12 Section 5 - Slide 3 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Empirical probability and theoretical probability Compound probability, conditional probability, and binomial probability Odds against an event and odds in favor of an event Expected value Tree diagrams

4. Chapter 12 Section 5 - Slide 4 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Mutually exclusive events and independent events The counting principle, permutations, and combinations

5. Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 5 - Slide 5 Section 5 Tree Diagrams

6. Chapter 12 Section 5 - Slide 6 Copyright © 2009 Pearson Education, Inc. Counting Principle If a first experiment can be performed in M distinct ways and a second experiment can be performed in N distinct ways, then the two experiments in that specific order can be performed in M N distinct ways.

7. Chapter 12 Section 5 - Slide 7 Copyright © 2009 Pearson Education, Inc. Definitions Sample space: A list of all possible outcomes of an experiment. Sample point: Each individual outcome in the sample space. Tree diagrams are helpful in determining sample spaces.

8. Chapter 12 Section 5 - Slide 8 Copyright © 2009 Pearson Education, Inc. Example Two balls are to be selected without replacement from a bag that contains one purple, one blue, and one green ball. a)Use the counting principle to determine the number of points in the sample space. b)Construct a tree diagram and list the sample space. c)Find the probability that one blue ball is selected. d)Find the probability that a purple ball followed by a green ball is selected.

9. Chapter 12 Section 5 - Slide 9 Copyright © 2009 Pearson Education, Inc. Solutions a) 3 2 = 6 ways b) c) d) B P B G B G P G P PB PG BP BG GP GB

10. Chapter 12 Section 5 - Slide 10 Copyright © 2009 Pearson Education, Inc. P(event happening at least once)