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# Section 0-4 Algebra 2

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The Counting Principle

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### Section 0-4 Algebra 2

1. 1. Section 0-4 The Counting Principle
2. 2. Essential Question How do you use the Fundamental Counting Principle to ﬁnd outcomes involving independent and dependent events?
3. 3. Vocabulary 1. Outcome: 2. Sample Space: 3. Event: 4. Independent: 5. Dependent:
4. 4. Vocabulary 1. Outcome: The result of a single trial 2. Sample Space: 3. Event: 4. Independent: 5. Dependent:
5. 5. Vocabulary 1. Outcome: The result of a single trial 2. Sample Space: The set of all possible outcomes 3. Event: 4. Independent: 5. Dependent:
6. 6. Vocabulary 1. Outcome: The result of a single trial 2. Sample Space: The set of all possible outcomes 3. Event: One or more outcomes of a trial 4. Independent: 5. Dependent:
7. 7. Vocabulary 1. Outcome: The result of a single trial 2. Sample Space: The set of all possible outcomes 3. Event: One or more outcomes of a trial 4. Independent: When the outcome of one event has no affect on the outcome of another event 5. Dependent:
8. 8. Vocabulary 1. Outcome: The result of a single trial 2. Sample Space: The set of all possible outcomes 3. Event: One or more outcomes of a trial 4. Independent: When the outcome of one event has no affect on the outcome of another event 5. Dependent: When the outcome of one event affects the outcome of another event
9. 9. Vocabulary 5. Fundamental Counting Principle (FCP): 6. Factorial:
10. 10. Vocabulary 5. Fundamental Counting Principle (FCP): If one event can occur in x ways and a second event in y ways, then completing the ﬁrst event then the second event can occur in xy ways 6. Factorial:
11. 11. Vocabulary 5. Fundamental Counting Principle (FCP): If one event can occur in x ways and a second event in y ways, then completing the ﬁrst event then the second event can occur in xy ways 6. Factorial: n! is the product of all counting numbers from n down through 1
12. 12. Example 1 Determine whether the following events are independent or dependent. a. Drawing a card from a deck and rolling a die b. Choosing a winner and runner-up in a bake off c. Choosing the color and brand of a pair of shoes
13. 13. Example 1 Determine whether the following events are independent or dependent. a. Drawing a card from a deck and rolling a die b. Choosing a winner and runner-up in a bake off c. Choosing the color and brand of a pair of shoes Independent
14. 14. Example 1 Determine whether the following events are independent or dependent. a. Drawing a card from a deck and rolling a die b. Choosing a winner and runner-up in a bake off c. Choosing the color and brand of a pair of shoes Independent Dependent
15. 15. Example 1 Determine whether the following events are independent or dependent. a. Drawing a card from a deck and rolling a die b. Choosing a winner and runner-up in a bake off c. Choosing the color and brand of a pair of shoes Independent Dependent Independent
16. 16. Example 2 Matt Mitarnowski is planning to buy a new computer. He can choose from ﬁve different storage options and four different colors. In how many ways can he create a computer to purchase?
17. 17. Example 2 Matt Mitarnowski is planning to buy a new computer. He can choose from ﬁve different storage options and four different colors. In how many ways can he create a computer to purchase? 5 ∙ 4
18. 18. Example 2 Matt Mitarnowski is planning to buy a new computer. He can choose from ﬁve different storage options and four different colors. In how many ways can he create a computer to purchase? 5 ∙ 4 = 20 ways
19. 19. Example 3 For a dinner in a restaurant, Maggie Brann can choose from 4 appetizers, 6 main courses, 5 beverages, and 3 desserts. How many different meal combinations are there?
20. 20. Example 3 For a dinner in a restaurant, Maggie Brann can choose from 4 appetizers, 6 main courses, 5 beverages, and 3 desserts. How many different meal combinations are there? 4 ∙ 6 ∙ 5 ∙ 3
21. 21. Example 3 For a dinner in a restaurant, Maggie Brann can choose from 4 appetizers, 6 main courses, 5 beverages, and 3 desserts. How many different meal combinations are there? 4 ∙ 6 ∙ 5 ∙ 3 = 360 meals
22. 22. Example 4 Fuzzy Jeff is planning to visit 5 colleges over the next two months. In how many different orders can he visit all 5 colleges?
23. 23. Example 4 Fuzzy Jeff is planning to visit 5 colleges over the next two months. In how many different orders can he visit all 5 colleges? 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1
24. 24. Example 4 Fuzzy Jeff is planning to visit 5 colleges over the next two months. In how many different orders can he visit all 5 colleges? 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 120 orders
25. 25. Summary Describe the difference between independent and dependent events.