The Fundamental Counting Principle

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The Fundamental Counting Principle

• 9.5

Pre-Algebra
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Warm Up
An experiment consists of rolling a fair number
cube with faces numbered 2, 4, 6, 8, 10, and 12.
Find each probability. 1. P(rolling an even
number) 2. P(rolling a prime number) 3. P(rolling
a number gt 7)
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Learn to find the number of possible outcomes in
an experiment.
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Vocabulary
Fundamental Counting Principal tree diagram
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(No Transcript)
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Example Using the Fundamental Counting Principal
License plates are being produced that have a
single letter followed by three digits. All
license plates are equally likely.
A. Find the number of possible license plates.
Use the Fundamental Counting Principal.
second digit
letter
first digit
third digit
26 choices
10 choices
10 choices
10 choices
26 ? 10 ? 10 ? 10 26,000
The number of possible 1-letter, 3-digit license
plates is 26,000.
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Example Using the Fundamental Counting Principal
B. Find the probability that a license plate has
the letter Q.
0.038
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Example Using the Fundamental Counting Principle
C. Find the probability that a license plate does
not contain a 3.
First use the Fundamental Counting Principle to
find the number of license plates that do not
contain a 3.
26 ? 9 ? 9 ? 9 18,954 possible license plates

without a 3
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Try This
Social Security numbers contain 9 digits. All
social security numbers are equally likely.
A. Find the number of possible Social Security
numbers.
Use the Fundamental Counting Principal.
10 ? 10 ? 10 ? 10 ? 10 ? 10 ? 10 ? 10 ? 10
10,000,000,000
The number of Social Security numbers is
10,000,000,000.
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Try This
B. Find the probability that the Social Security
number contains a 7.
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Try This
C. Find the probability that a Social Security
number does not contain a 7.
First use the Fundamental Counting Principle to
find the number of Social Security numbers that
do not contain a 7.
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The Fundamental Counting Principle tells you only
the number of outcomes in some experiments, not
what the outcomes are. A tree diagram is a way to
show all of the possible outcomes.
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Example Using a Tree Diagram
You have a photo that you want to mat and frame.
You can choose from a blue, purple, red, or green
mat and a metal or wood frame. Describe all of
the ways you could frame this photo with one mat
and one frame.
You can find all of the possible outcomes by
making a tree diagram.
There should be 4 ? 2 8 different ways to frame
the photo.
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Example Continued
Each branch of the tree diagram represents a
different way to frame the photo. The ways shown
in the branches could be written as (blue,
metal), (blue, wood), (purple, metal), (purple,
wood), (red, metal), (red, wood), (green, metal),
and (green, wood).
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Try This
A baker can make yellow or white cakes with a
choice of chocolate, strawberry, or vanilla
icing. Describe all of the possible combinations
of cakes.
You can find all of the possible outcomes by
making a tree diagram. There should be 2 ? 3 6
different cakes available.
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Try This
yellow cake
The different cake possibilities are (yellow,
chocolate), (yellow, strawberry), (yellow,
vanilla), (white, chocolate), (white,
strawberry), and (white, vanilla).
vanilla icing
chocolate icing
strawberry icing
white cake
vanilla icing
chocolate icing
strawberry icing
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Lesson Quiz
Personal identification numbers (PINs) contain 2
letters followed by 4 digits. Assume that all
codes are equally likely. 1. Find the number of
possible PINs. 2. Find the probability that a
PIN does not contain a 6. 3. For lunch a student
can choose one sandwich, one bowl of soup, and
one piece of fruit. The choices include grilled
cheese, peanut butter, or turkey sandwich,
chicken soup or clam chowder, and an apple,
banana, or orange. How many different lunches are
possible?
6,760,000
0.6561
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