1. The Counting Principle & Finding Sets
Probability
The Counting Principle & Finding Sets

2. Use an appropriate method to find the number of outcomes in each of the following situations:
1. Your school cafeteria offers chicken or tuna sandwiches; chips or fruit; and milk, apple juice, or orange juice. If you purchase one sandwich, one side item and one drink, how many different lunches can you choose?
There are 12 possible lunches.
Sandwich(2) Side Item(2) Drink(3) Outcomes
apple juice orange juice milk
chicken, chips, apple chicken, chips, orange chicken, chips, milk
chicken, fruit, apple chicken, fruit, orange chicken, fruit, milk
tuna, chips, apple tuna, chips, orange tuna, chips, milk
tuna, fruit, apple tuna, fruit, orange tuna, fruit, milk
chips
fruit
chicken
tuna
chips
fruit

3. (2 sandwiches, 2 sides, 3 drinks)
Easier Way
No need to make the tree diagram.
Multiply each of the number of choices
(2 sandwiches, 2 sides, 3 drinks)

4. Counting Principle
At a sporting goods store, skateboards are available in 8 different deck designs. Each deck design is available with 4 different wheel assemblies. How many skateboard choices does the store offer? 32

5. Counting Principle
A father takes his son, Marcus, to Wendy’s for lunch. He tells Marcus he can get a 5 piece nuggets, a spicy chicken sandwich, or a single for the main entrée. For sides, he can get fries, a side salad, potato, or chili. And for drinks, he can get a frosty, coke, sprite, or an orange drink. How many options for meals does Marcus have? 48

6. I-Pods can vary the order in which songs are played
I-Pods can vary the order in which songs are played. Your I-Pod currently only contains 8 songs. Find the number of orders in which the songs can be played.
There are 40,320 possible song orders.
1st Song nd rd th th th th th Outcomes
In this situation it makes more sense to use the Fundamental Counting Principle. 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 =
40,320
The solutions in examples 3 and 4 involve the product of all the integers from n to one. The product of all positive integers less than or equal to a number is a factorial.

7. Set Notation

8. Probability A number from 0 to 1 As a percent from 0% to 100%
Indicates how likely an event will occur

9. Diagram from Walch Education

10. Experiment Any process or action that has observable results.
Example: drawing a card from a deck of cards is an experiment

11. Outcomes Results from experiments
Example: all the cards in the deck are possible outcomes

12. Sample Space The set (or list) of all possible outcomes.
Also known as the universal set
Example: listing out all the cards in the deck would be the sample space

13. Event A subset of an experiment An outcome or set of desired outcomes
Example: drawing a single Jack of hearts

14. Set
List or collection of items

15. Subset List or collection of items all contained within another set
Denoted by AB, if all the elements of A are also in B.

16. Subset

17. Example Let A be all multiples of 4 and B be all multiples of 2.
Is A a subset of B? And is B a subset of A?
A = {..., -8, -4, 0, 4, 8, ...}
B = {..., -8, -6, -4, -2, 0, 2, 4, 6, 8, ...}

18. Empty Set A set that has NO elements Also called a null set.
Denoted by 
As an example, think of the set of piano keys on a guitar.