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