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

AND

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

Chapter 12

Probability

Chapter 12 Section 5 - Slide 3Copyright © 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

Chapter 12 Section 5 - Slide 4Copyright © 2009 Pearson Education, Inc.

WHAT YOU WILL LEARN• Mutually exclusive events and

independent events• The counting principle,

permutations, and combinations

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

Section 5

Tree Diagrams

Chapter 12 Section 5 - Slide 6Copyright © 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.

Chapter 12 Section 5 - Slide 7Copyright © 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.

Chapter 12 Section 5 - Slide 8Copyright © 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.

Chapter 12 Section 5 - Slide 9Copyright © 2009 Pearson Education, Inc.

Solutions

a) 3 • 2 = 6 waysb)

c)

d)

B

P

B

G

BG

PGP

PBPGBP

BGGP

GB

P blue 4

6

23

P Purple,Green P P,G 1

6

Chapter 12 Section 5 - Slide 10Copyright © 2009 Pearson Education, Inc.

P(event happening at least once)

P

event happeningat least once

1 P

event doesnot happen