Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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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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Problem of the Day There are 10 players in a
chess tournament. How many games are needed for
each player to play every other player one time?
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Learn to find the number of possible outcomes in
an experiment.
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Insert Lesson Title Here
Vocabulary
Fundamental Counting Principle tree
diagram Addition Counting Principle
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(No Transcript)
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Additional Example 1A Using the Fundamental
Counting Principle
License plates are being produced that have a
single letter followed by three digits. All
license plates are equally likely.
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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Additional Example 1B Using the Fundamental
Counting Principal
Find the probability that a license plate has the
letter Q.
0.038
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Additional Example 1C Using the Fundamental
Counting Principle
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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Check It Out Example 1A
Social Security numbers contain 9 digits. All
social security numbers are equally likely.
Find the number of possible Social Security
numbers.
Use the Fundamental Counting Principle.
Digit 1 2 3 4 5 6 7 8 9
Choices 10 10 10 10 10 10 10 10 10
10 10 10 10 10 10 10 10 10
1,000,000,000
The number of Social Security numbers is
1,000,000,000.
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Check It Out Example 1B
Find the probability that the Social Security
number contains a 7.
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Check It Out Example 1C
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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Additional Example 2 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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Additional Example 2 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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Check It Out Example 2
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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Check It Out Example 2 Continued
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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Additional Example 3 Using the Addition Counting
Principle
The table shows the items available at a farm
stand. How many items can you choose from the
farm stand?
Apples Pears Squash
Macintosh Bosc Acorn
Red Delicious Yellow Bartlett Hubbard
Gold Delicious Red Bartlett
None of the lists contains identical items, so
use the Addition Counting Principle.
Total Choices
Apples
Pears
Squash



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Additional Example 3 Continued
T
3
3
2



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There are 8 items to choose from.
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Check It Out Example 3
The table shows the items available at a clothing
store. How many items can you choose from the
clothing store?
T-Shirts Sweaters Pants
Long Sleeve Wool Denim
Shirt Sleeve Cotton Khaki
Pocket Polyester
Cashmere
None of the lists contains identical items, so
use the Addition Counting Principle.
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Additional Example 3 Continued
Total Choices
T-shirts
Sweaters
Pants



T
3
4
2



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There are 9 items to choose from.
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Insert Lesson Title Here
Lesson Quiz Part I
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.
6,760,000
0.6561
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Insert Lesson Title Here
Lesson Quiz Part II
A lunch menu consists of 3 types of sandwiches, 2
types of soup, and 3 types of fruit. 3. What is
the total number of lunch items on the t menu?
4. A student wants to order one sandwich, one
t bowl of soup, and one piece of fruit.
How many t different lunches are possible?
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