12.4 counting methods 1

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12.4 counting methods 1

  1. 1. Lesson 12.4, For use with pages 670-674 1. Find the probability of rolling a number less than 5 on a dice. 2. Find the probability of rolling a number less than 7 on a dice.
  2. 2. Lesson 12.4, For use with pages 670-674 1. Find the probability of rolling a number less than 5 on a dice. 3 2ANSWER 2. Find the probability of rolling a number less than 7 on a dice. 0ANSWER
  3. 3. Tree Diagrams and the Counting Principle Section 12.4
  4. 4. Essential Questions • What are the differences between permutations and combinations? • What are the differences between odds and probability? • How is probability used to make predictions? • What are the differences between experimental and theoretical probabilities?
  5. 5. • Today we will be learning about different ways to “count” difficult situations. The two methods we will use will be 1) Tree Diagrams 2) The Counting Principle
  6. 6. Vocabulary • Tree diagram: a branching diagram that shows all the possible choices or outcomes of a process carried out in several stages.
  7. 7. • At Sam’s Deli, you can make a sub sandwich using the following: Breads: wheat, rye Meat: ham, turkey, salami How many ways can you put a sandwich together? Use a tree diagram
  8. 8. Breads: wheat, rye Meat: ham, turkey, salami Wheat Rye H T S H T S
  9. 9. Breads: wheat, rye Meat: ham, turkey, salami Now if we added cheese to the sandwich. Cheese: cheddar, American, Swiss Wheat Rye H T S H T S C A S C A S C A S C A S C A S C A S
  10. 10. EXAMPLE 1 Making a Tree Diagram Make a tree diagram to help you choose an outfit. You can choose a T-shirt (T), button-down shirt (B), sweater (S), or a polo (P) as a top, and jeans (J), khakis (K), or dress pants (D) for pants. How many different outfits are possible? There are 12 different possible outfits.
  11. 11. • The “Counting Principle” states “if a situation can occur in m ways, and a second situation can occur in n ways, then these things can occur together in “m x n” ways.
  12. 12. EXAMPLE 2 Using the Counting Principle Skateboards ANSWER You can build 15 different skateboards. 5 3 = 15 decks wheel assemblies To build a skateboard, you can choose one deck and one type of wheel assembly from those shown. To count the number of different skateboards you can build, use the counting principle.
  13. 13. • How many different results could you get by spinning both spinners below? – 4 x 3 = 12 1 2 3 4 Blue Green Red
  14. 14. EXAMPLE 3 Using the Counting Principle Passwords You are choosing a password that starts with 3 letters and then has 2 digits. How many different passwords are possible? SOLUTION 26 26 26 10 10 = letters digits ANSWER There are 1,757,600 different possible passwords. 1,757,600
  15. 15. EXAMPLE 3 Using the Counting Principle Passwords You are choosing a password that starts with 3 letters and then has 2 digits. How many different passwords are possible? 26 26 26 10 10 = letters digits 1,757,600 How would the number of possible passwords change if you were to add one letter to the requirement? 26 x 26 x 26 x 26 x 10 x 10 = 45,697,600
  16. 16. GUIDED PRACTICE for Example 1, 2, and 3 2. Soccer Uniforms Your soccer team’s uniform choices include yellow and green shirts, white, black, and green shorts, and four colors of socks. How many different uniforms are possible? Soccer team have 2 shirts 3 shorts and 4 socks to select. Use the counting principle. ANSWER The number of possible uniform are 2 3 4 = 24 uniform
  17. 17. Probability Number of favorable outcomes Number of possible outcomes
  18. 18. EXAMPLE 4 Solve a Multi-Step Problem Number Cubes You and three friends each roll a number cube. What is the probability that you each roll the same number? STEP 1 List the favorable outcomes. There are 6: Everyone could roll 1-1-1-1, 2-2-2-2, 3-3-3-3, 4-4-4-4, 5-5-5-5, or 6-6-6-6. STEP 2 Find the number of possible outcomes using the counting principle. 6 6 6 6 = 1296 4 number cubes
  19. 19. EXAMPLE 4 Solve a Multi-Step Problem STEP 3 Find the probability: Number of favorable outcomes Number of possible outcomes = 1296 6 = 216 1 ANSWER The probability that you each roll the same number is . 216 1
  20. 20. Homework • Page 672 #1-12

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