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

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) Course Counting Principles

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 Counting Principles

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

Vocabulary Fundamental Counting Principle tree diagram Addition Counting Principle Insert Lesson Title Here Course Counting Principles

Course Counting Principles

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 = 26,000 The number of possible 1-letter, 3-digit license plates is 26,000. Course Counting Principles

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 Choices = 1,000,000,000 The number of Social Security numbers is 1,000,000,000. Course Counting Principles

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

Check It Out: Example 2B Find the probability that the Social Security number contains a 7. P(7 _ _ _ _ _ _ _ _) = ,000,000,000 = = Course Counting Principles

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 = 18,954 possible license plates without a 3 There are 9 choices for any digit except 3. P(no 3) = = ,000 18,954 Course Counting Principles

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 _ _ _ _ _ _ _ _) = ,000,000,000 P(no 7) = ≈ 0.4 1,000,000, ,420,489 Course Counting Principles

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 Counting Principles

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 Counting Principles

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 Counting Principles

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 Counting Principles

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 Counting Principles

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 Counting Principles