d2.b how do i apply the fundamental & addition counting principles to find the number of...
TRANSCRIPT
![Page 1: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/1.jpg)
D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes?
Course 3
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
![Page 2: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/2.jpg)
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
![Page 3: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/3.jpg)
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
![Page 4: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/4.jpg)
Learn to find the number of possible outcomes in an experiment.
Course 3
10-8 Counting Principles
![Page 5: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/5.jpg)
Vocabulary
Fundamental Counting Principletree diagramAddition Counting Principle
Insert Lesson Title Here
Course 3
10-8 Counting Principles
![Page 6: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/6.jpg)
Course 3
10-8 Counting Principles
![Page 7: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/7.jpg)
License plates are being produced that have a single letter followed by three digits. All license plates are equally likely.
Example 1: Using the Fundamental Counting Principle
**Find the number of possible license plates.
Use the Fundamental Counting Principle.
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
![Page 8: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/8.jpg)
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
![Page 9: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/9.jpg)
Example 2: Using the Fundamental Counting Principle
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
![Page 10: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/10.jpg)
Check It Out: Example 2B
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
![Page 11: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/11.jpg)
Example 3: Using the Fundamental Counting Principle
Find the probability that a license plate, with a single letter followed by three digits, 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
![Page 12: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/12.jpg)
Check It Out: Example 3A
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
![Page 13: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/13.jpg)
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
![Page 14: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/14.jpg)
Example 4: 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
![Page 15: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/15.jpg)
Additional Example 4 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
![Page 16: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/16.jpg)
Check It Out: Example 4A
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
![Page 17: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/17.jpg)
Check It Out: Example 4A 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
![Page 18: D2.b How Do I Apply the Fundamental & Addition Counting Principles To Find The Number of Outcomes? Course 3 Warm Up Warm Up Problem of the Day Problem](https://reader036.vdocuments.site/reader036/viewer/2022062321/56649eca5503460f94bd7bbd/html5/thumbnails/18.jpg)
Lesson Quiz
A lunch menu consists of 3 types of sandwiches, 2 types of soup, and 3 types of fruit.
1. What is the total number of lunch items on the t menu?
2. 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
Insert Lesson Title Here
Course 3
10-8 Counting Principles