1. 10-8 Counting Principles 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. Learn to find the number of possible outcomes in an experiment. Course 3 10-8 Counting Principles

4. 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. letterfirst digit second digit third digit (26 choices)(10 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 License plates

5. 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 What you are looking for. Total possible outcomes. License plates are being produced that have a single letter followed by three digits. P( Q, any number, any number, any number) = Use the Fundamental Counting Principal.

6. Find the probability that a license plate does not contain a 3. 26 9 9 9 = 18,954 possible license plates without a 3. There are 9 choices for any digit other than 3. P(no 3) = = 0.729 26,000 18,954 Course 3 10-8 Counting Principles License plates are being produced that have a single letter followed by three digits. P( any letter, no 3, no 3, no 3) =

7. 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 1st2nd3rd4th5th6th7th8th9th 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 Social Security

8. Find the probability that the social security number contains a 7. 1 10 10 10 10 10 10 10 10 1,000,000,000 = = 0.1 10 1 Course 3 10-8 Counting Principles Use the Fundamental Counting Principle. P(7 _ _ _ _ _ _ _ _) =

9. 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, no 7, no 7, no 7, no 7, no 7, no 7, no 7, 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

10. The Fundamental Counting Principle tells you only the number of outcomes, not what the outcomes are. A tree diagram is a way to show all of the possible outcomes. Course 3 10-8 Counting Principles

11. You have a photo that you want to mat and frame. You can choose from blue, purple, red, or green mats and a metal or wooden frame. Describe all of the ways you could frame this photo with one mat and one frame. Course 3 10-8 Counting Principles You can use the counting principle to see how many choices there are. 4 colors for the mat. 2 choices of frames. 4 2 = 8 There should be 8 different ways to frame the photo. Photo

12. Course 3 10-8 Counting Principles You can find all of the possible outcomes by making a tree diagram. _________ ____ _____ ____ __________ Photo

13. 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

14. 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 Cakes

15. 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

16. A movie theater sells popcorn in small, medium, or large containers. Each size is also available for regular or lightly buttered popcorn. 1.Draw a tree diagram to show the possible options for buying popcorn at the movie theater? 2. How many options are there if the theater adds two new flavors: cheddar cheese and caramel?

17. Bread = white or wheat Meat = ham,roast beef,or tuna Cheese= american or swiss 1.How many possible outcomes are there? 2. What principle did you use to determine the number of possible outcomes? 3. Draw a tree diagram to show the possible outcomes.

18. Let’s Think…. Suppose a teacher wants to choose two different students to run errands—one to go to the library and one to go to the office. Out of a class of 30, how many possible combinations of two students are there? BE CAREFUL: Some people might think: 2 x 30 = 60 The answer is_______.

19. 30 x 29 = 870

20. Mrs. Love’s Children Part I: Your next door neighbor, Mrs. Love, is expecting twins. She has picked out names for two girls, but is having difficulty thinking of any boy names. Since she knows that there is a possibility of having at least one boy, she wants you to help her determine some possible names. A.Make a list of your five favorite boy names. B. Using the names that you have chosen, tell how many ways she could name a boy baby using both a first name and a middle name from your list.

21. Answers to part I You came up with 5 names. You do not want to use a name more than once (ex. Kevin Kevin). The task of naming a boy child represents a situation of drawing more than once from the same set without having repetitions. You would multiply the number of possible first names by the number of possible middle names. 5 first names multiplied by 4 middle names 5 4 = 20

22. 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. 0.6561 6,760,000 Insert Lesson Title Here Course 3 10-8 Counting Principles

23. Lesson Quiz: Part II A lunch menu consists of 3 types of sandwiches, 2 types of soup, and 3 types of fruit. 3. A student wants to order one sandwich, one t bowl of soup, and one piece of fruit. How many t different lunches are possible? 4.Create a tree diagram using your own choices of sandwiches, soups, and fruits. 18 Insert Lesson Title Here Course 3 10-8 Counting Principles