Post on 16-Dec-2015
10-8 Counting Principles
Course 3
Warm Up
Problem of the Day
Lesson Presentation
Warm UpAn 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 > 7)
11612
Course 3
10-8 Counting Principles
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?45
Course 3
10-8 Counting Principles
Learn to find the number of possible outcomes in an experiment.
Course 3
10-8 Counting Principles
Vocabulary
Fundamental Counting Principletree diagramAddition Counting Principle
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Course 3
10-8 Counting Principles
Course 3
10-8 Counting Principles
License plates are being produced that have a single letter followed by three digits. All license plates are equally likely.
Additional Example 1A: Using the Fundamental Counting Principle
Find the number of possible license plates.
Use the Fundamental Counting Principal.
letter first digit second digit third digit
26 choices 10 choices 10 choices 10 choices
26 • 10 • 10 • 10 = 26,000The number of possible 1-letter, 3-digit license plates is 26,000.
Course 3
10-8 Counting Principles
Additional Example 1B: Using the Fundamental Counting Principal
Find the probability that a license plate has the letter Q.
1 • 10 • 10 • 1026,000 =
1 26
0.038P(Q ) =
Course 3
10-8 Counting Principles
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 3There are 9 choices for any digit except 3.
P(no 3) = = 0.72926,00018,954
Course 3
10-8 Counting Principles
Social Security numbers contain 9 digits. All social security numbers are equally likely.
Check It Out: Example 1A
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 = 1,000,000,000The number of Social Security numbers is 1,000,000,000.
Course 3
10-8 Counting Principles
Check It Out: Example 1B
Find the probability that the Social Security number contains a 7.
P(7 _ _ _ _ _ _ _ _) = 1 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 1,000,000,000
= = 0.1 10
1
Course 3
10-8 Counting Principles
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.
P(no 7 _ _ _ _ _ _ _ _) = 9 • 9 • 9 • 9 • 9 • 9 • 9 • 9 • 9 1,000,000,000
P(no 7) = ≈ 0.4 1,000,000,000
387,420,489
Course 3
10-8 Counting Principles
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.
Course 3
10-8 Counting Principles
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.
Course 3
10-8 Counting Principles
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).
Course 3
10-8 Counting Principles
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.
Course 3
10-8 Counting Principles
Check It Out: Example 2 Continued
The different cake possibilities are (yellow, chocolate), (yellow, strawberry), (yellow, vanilla), (white, chocolate), (white, strawberry), and (white, vanilla).
white cake
yellow cake
chocolate icing
vanilla icing
strawberry icing
chocolate icing
vanilla icing
strawberry icing
Course 3
10-8 Counting Principles
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?
None of the lists contains identical items, so use the Addition Counting Principle.
Total Choices
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10-8 Counting Principles
Apples Pears Squash+= +
Apples Pears Squash
Macintosh Bosc Acorn
Red Delicious Yellow Bartlett Hubbard
Gold Delicious Red Bartlett
Additional Example 3 Continued
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10-8 Counting Principles
T 3 3 2+= + = 8
There are 8 items to choose from.
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?
None of the lists contains identical items, so use the Addition Counting Principle.
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10-8 Counting Principles
T-Shirts Sweaters Pants
Long Sleeve Wool Denim
Shirt Sleeve Cotton Khaki
Pocket Polyester
Cashmere
Additional Example 3 Continued
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10-8 Counting Principles
T 3 4 2+= + = 9
There are 9 items to choose from.
Total Choices T-shirts Sweaters Pants+= +
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 containa 6. 0.6561
6,760,000
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Course 3
10-8 Counting Principles
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?
18
8
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Course 3
10-8 Counting Principles