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1. 10-8 Counting Principles Course 3 Warm Up Problem of the Day Lesson Presentation

2. 10-8 Counting Principles 1 1 6 2 Course 3 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 > 7) 1

3. 10-8 Counting Principles Course 3 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

4. 10-8 Counting Principles Course 3 Learn to find the number of possible outcomes in an experiment.

5. 10-8 Counting Principles Course 3 Insert Lesson Title Here Vocabulary Fundamental Counting Principle tree diagram Addition Counting Principle

6. 10-8 Counting Principles Course 3

7. 10-8 Counting Principles Course 3 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.

8. 10-8 Counting Principles 1 • 10 •10 • 10 26,000 P(Q ) = =  1 26 Course 3 Additional Example 1B: Using the Fundamental Counting Principal Find the probability that a license plate has the letter Q. 0.038

9. 10-8 Counting Principles There are 9 choices for any digit except 3. 18,954 P(no 3) = = 0.729 26,000 Course 3 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

10. 10-8 Counting Principles Course 3 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. 10 • 10 •10 • 10 • 10 • 10 • 10 • 10 • 10 = 1,000,000,000 The number of Social Security numbers is 1,000,000,000.

11. 10-8 Counting Principles P(7 _ _ _ _ _ _ _ _) = 1 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 1,000,000,000 1 = = 0.1 10 Course 3 Check It Out: Example 1B Find the probability that the Social Security number contains a 7.

12. 10-8 Counting Principles P(no 7 _ _ _ _ _ _ _ _) = 9 • 9 • 9 • 9 • 9 • 9 • 9 • 9 • 9 1,000,000,000 387,420,489 P(no 7) = ≈ 0.4 1,000,000,000 Course 3 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.

13. 10-8 Counting Principles Course 3 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.

14. 10-8 Counting Principles Course 3 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.

15. 10-8 Counting Principles Course 3 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).

16. 10-8 Counting Principles Course 3 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.

17. 10-8 Counting Principles Course 3 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

18. 10-8 Counting Principles Course 3 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 = Apples + Pears + Squash

19. 10-8 Counting Principles Course 3 Additional Example 3 Continued T = 3 + 3 + 2 = 8 There are 8 items to choose from.

20. 10-8 Counting Principles Course 3 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.

21. 10-8 Counting Principles Course 3 Additional Example 3 Continued Total Choices = T-shirts + Sweaters + Pants T = 3 + 4 + 2 = 9 There are 9 items to choose from.

22. 10-8 Counting Principles Course 3 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

23. 10-8 Counting Principles Course 3 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? 8 18