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 of the Day Lesson Presentation Lesson Presentation

2. 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 1 6 1 2 Course 3 10-8 Counting Principles

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 Course 3 10-8 Counting Principles

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

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

6. Course 3 10-8 Counting Principles

7. 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. letterfirst digit second digit third digit 26 choices10 choices 26 10 10 10 = 26,000 The number of possible 1-letter, 3-digit license plates is 26,000. Course 3 10-8 Counting Principles

8. 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. Digit123456789 Choices10 10 10 10 10 10 10 10 10 10 = 1,000,000,000 The number of Social Security numbers is 1,000,000,000. Course 3 10-8 Counting Principles

9. Example 2: Using the Fundamental Counting Principle Find the probability that a license plate has the letter Q. 1 10 10 10 26,000 = 1 26  0.038 P(Q ) = Course 3 10-8 Counting Principles

10. 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

11. 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 3 There are 9 choices for any digit except 3. P(no 3) = = 0.729 26,000 18,954 Course 3 10-8 Counting Principles

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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