1. Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 5 - Slide 1 P-5 Probability Tree Diagrams

2. Chapter 12 Section 5 - Slide 2 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Tree diagrams The counting principle

3. Chapter 12 Section 5 - Slide 3 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.

4. Chapter 12 Section 5 - Slide 4 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.

5. Chapter 12 Section 5 - Slide 5 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.

6. Chapter 12 Section 5 - Slide 6 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

7. Chapter 12 Section 5 - Slide 7 Copyright © 2009 Pearson Education, Inc. P(event happening at least once)

8. Chapter 12 Section 5 - Slide 8 Copyright © 2009 Pearson Education, Inc. Dice Exercise Create a tree and develop probabilities for all events for the following: 2 dice 3 dice

9. Slide 12 - 9 Copyright © 2009 Pearson Education, Inc. At the bakery, a box of cookies is made by selecting four cookies from the six types of cookie - chocolate chip, oatmeal raisin, sugar, peanut butter, butterscotch, and chocolate. In how many ways can a box of cookies be put together? a.360 b.30 c.15 d.6

10. Slide 12 - 10 Copyright © 2009 Pearson Education, Inc. At the bakery, a box of cookies is made by selecting four cookies from the six types of cookie - chocolate chip, oatmeal raisin, sugar, peanut butter, butterscotch, and chocolate. In how many ways can a box of cookies be put together? a.360 b.30 c.15 d.6

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

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