Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

1. P(rolling an even number) 2. P(rolling a prime number) 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

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

Learn to find the number of possible outcomes in an experiment.

Vocabulary Fundamental Counting Principle tree diagram

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. letter first digit second 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.

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

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 There are 9 choices for any digit except 3. P(no 3) = = 0.729 26,000 18,954

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. Digit 1 2 3 4 5 6 7 8 9 Choices 10 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 = 1,000,000,000 The number of Social Security numbers is 1,000,000,000.

Find the probability that the Social Security number contains a 7. 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

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

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.

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.

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).

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.

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

Additional Example 3: Using a Tree Diagram for Dependent Events There are 7 black socks and 2 white socks in a drawer. Two socks are removed. What is the probability that the colors match? A pair of socks of the same color is a match. After the first sock is selected, the probability of selecting another sock of the same color changes. Make a tree diagram showing the probably of each outcome.

Additional Example 3 Continued 9 choices for first sock 8 choices for second sock Multiply to find the probability for each outcome 68 34 = 79 34 7 12 = 79 28 14 = 79 14 7 36 = 78 29 78 7 36 = 29 29 18 1 36 = 18

Additional Example 3 Continued The probability of drawing a matching pair is

Check It Out: Example 3 There are 5 black socks and 3 white socks in a drawer. Two socks are removed. What is the probability that the colors match? A pair of socks of the same color is a match. After the first sock is selected, the probability of selecting another sock of the same color changes. Make a tree diagram showing the probably of each outcome.

Check It Out: Example 3 Continued 8 choices for first sock 7 choices for second sock Multiply to find the probability for each outcome 47 58 47 5 14 = 58 37 58 37 15 56 = 57 38 57 15 56 = 38 27 38 27 3 28 =

Check It Out: Example 3 Continued The probability of drawing a matching pair is

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 24

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

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

Lesson Quiz for Student Response Systems 1. A login password contains 3 letters followed by 2 digits. Identify the number of possible login passwords. A. 175,760 B. 676,000 C. 1,757,600 D. 6,760,000 27

Lesson Quiz for Student Response Systems 2. Employee identification codes at a company contain 2 letters followed by 4 digits. Assume that all codes are equally likely. Identify the probability that an ID code does not contain the letter I. A. 0.6567 B. 0.7493 C. 0.8321 D. 0.9246 28

Lesson Quiz for Student Response Systems 3. A restaurant offers 4 main courses, 3 desserts, and 5 types of juices. What is the total number of items on the menu? A. 3 B. 7 C. 9 D. 12 29

Lesson Quiz for Student Response Systems 4. A restaurant offers 3 types of starters, 4 types of sandwiches, and 4 types of salads for dinner. Visitors select one starter, one sandwich, and one salad. How many different dinners are possible? A. 3 B. 4 C. 11 D. 48 30