The Fundamental Counting Principle

Transcription

1 LESSON 10-6 The Fundamental Counting Principle Lesson Objectives Find the number of possible outcomes in an experiment Vocabulary Fundamental Counting Principle (p. 558) tree diagram (p. 559) Additional Examples Example 1 A. Find the number of possible license plates. Use the Counting Principle. letter first digit second digit third digit choices choices choices choices The number of possible 1-letter, 3-digit license plates is. B. Find the probability that a license plate has the letter Q. P(Q ) Holt McDougal Mathematics

2 C. Find the probability that a license plate does not contain a 3. There are choices for any digit except possible license plates without a 3. P(no 3) 26,000 Example 2 You have a photo that you want to mat and frame. You can choose from a blue, purple, red, or green mat and a or 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. There should be different ways to frame the photo. Each branch of the tree diagram represents a different way to frame the photo. The ways shown in the branches could be written as 235 Holt McDougal Mathematics

3 Example 3 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 colors 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 probability of each outcome. 9 choices for 8 choices for the Multiply to find the probability of the first sock second sock each outcome 7 1 The probability of drawing a pair of socks that match is Check It Out! 1. Social Security numbers contain 9 digits. All social security numbers are equally likely. Find the number of possible Social Security numbers. 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. 236 Holt McDougal Mathematics

4 LESSON 10-6 The Fundamental Counting Principle Lesson Objectives Find the number of possible outcomes in an experiment Vocabulary Fundamental Counting Principle (p. 558) If one event has m possible outcomes and a second event has n possible outcomes after the first event has occurred, then there are m n total possible outcomes for the two events. tree diagram (p. 559) A branching diagram that shows all possible combinations or outcomes of an event. Additional Examples Example 1 A. Find the number of possible license plates. Use the Fundamental Counting Principle. letter first digit second digit third digit 26 choices 10 choices 10 choices 10 choices ,000 The number of possible 1-letter, 3-digit license plates is 26,000. B. Find the probability that a license plate has the letter Q. P(Q ) , Holt McDougal Mathematics

5 C. Find the probability that a license plate does not contain a 3. There are 9 choices for any digit except , possible license plates without a 3. 18, P(no 3) 26,000 1, Example 2 You have a photo that you want to mat and frame. You can choose from a blue, purple, red, or green mat and a or frame. Describe all of the ways you could frame this photo with one mat and one frame. You can find all of the possible Photo outcomes by making a tree diagram. There should be 4 2 blue purple red green 8 different ways to frame the photo. 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, ), (blue, ), (purple, ), (purple, ), (red, ), (red, ), (green, ), and (green, ) 235 Holt McDougal Mathematics

6 Example 3 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 colors 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 probability of each outcome. 9 choices for 8 choices for the Multiply to find the probability of the first sock second sock each outcome The probability of drawing a pair of socks that match is Check It Out! 1. Social Security numbers contain 9 digits. All social security numbers are equally likely. Find the number of possible Social Security numbers. 1,000,000, 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. The different cake possibilities are (yellow, chocolate), (yellow, strawberry), (yellow, vanilla), (white, chocolate), (white, strawberry), and (white, vanilla). 236 Holt McDougal Mathematics