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Section 0-4
The Counting Principle
Essential Question
How do you use the Fundamental Counting Principle to
find outcomes involving independent and dependent
e...
Vocabulary
1. Outcome:
2. Sample Space:
3. Event:
4. Independent:
5. Dependent:
Vocabulary
1. Outcome: The result of a single trial
2. Sample Space:
3. Event:
4. Independent:
5. Dependent:
Vocabulary
1. Outcome: The result of a single trial
2. Sample Space: The set of all possible outcomes
3. Event:
4. Indepen...
Vocabulary
1. Outcome: The result of a single trial
2. Sample Space: The set of all possible outcomes
3. Event: One or mor...
Vocabulary
1. Outcome: The result of a single trial
2. Sample Space: The set of all possible outcomes
3. Event: One or mor...
Vocabulary
1. Outcome: The result of a single trial
2. Sample Space: The set of all possible outcomes
3. Event: One or mor...
Vocabulary
5. Fundamental Counting Principle (FCP):
6. Factorial:
Vocabulary
5. Fundamental Counting Principle (FCP): If one event
can occur in x ways and a second event in y ways,
then co...
Vocabulary
5. Fundamental Counting Principle (FCP): If one event
can occur in x ways and a second event in y ways,
then co...
Example 1
Determine whether the following events are
independent or dependent.
a. Drawing a card from a deck and rolling a...
Example 1
Determine whether the following events are
independent or dependent.
a. Drawing a card from a deck and rolling a...
Example 1
Determine whether the following events are
independent or dependent.
a. Drawing a card from a deck and rolling a...
Example 1
Determine whether the following events are
independent or dependent.
a. Drawing a card from a deck and rolling a...
Example 2
Matt Mitarnowski is planning to buy a new computer.
He can choose from five different storage options
and four di...
Example 2
Matt Mitarnowski is planning to buy a new computer.
He can choose from five different storage options
and four di...
Example 2
Matt Mitarnowski is planning to buy a new computer.
He can choose from five different storage options
and four di...
Example 3
For a dinner in a restaurant, Maggie Brann can
choose from 4 appetizers, 6 main courses, 5
beverages, and 3 dess...
Example 3
For a dinner in a restaurant, Maggie Brann can
choose from 4 appetizers, 6 main courses, 5
beverages, and 3 dess...
Example 3
For a dinner in a restaurant, Maggie Brann can
choose from 4 appetizers, 6 main courses, 5
beverages, and 3 dess...
Example 4
Fuzzy Jeff is planning to visit 5 colleges over the next
two months. In how many different orders can he visit
a...
Example 4
Fuzzy Jeff is planning to visit 5 colleges over the next
two months. In how many different orders can he visit
a...
Example 4
Fuzzy Jeff is planning to visit 5 colleges over the next
two months. In how many different orders can he visit
a...
Summary
Describe the difference between independent and
dependent events.
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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.

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