The document discusses the fundamental counting principle and how to use it to find outcomes involving independent and dependent events. It defines key terms like outcome, sample space, event, independent events which are those whose outcomes do not affect one another, and dependent events where one outcome affects another. Examples are provided to demonstrate determining if events are independent or dependent and using the counting principle to calculate the number of possible outcomes for scenarios involving choosing options.

1. Section 0-4
The Counting Principle

2. Essential Question
How do you use the Fundamental Counting Principle to
find outcomes involving independent and dependent
events?

3. Vocabulary
1. Outcome:
2. Sample Space:
3. Event:
4. Independent:
5. Dependent:

4. Vocabulary
1. Outcome: The result of a single trial
2. Sample Space:
3. Event:
4. Independent:
5. Dependent:

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. 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. 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. 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. Vocabulary
5. Fundamental Counting Principle (FCP):
6. Factorial:

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Summary
Describe the difference between independent and
dependent events.