1. Make and use sample spaces and use the counting principle.

2. Sample space All possible outcomes
Used to find the probability of an event.
Ex: create a table to find the sample space for rolling 2 dice. Outcomes are written as ordered pairs.
There are 36 possible outcomes
P(at least one 3)
There are 11 possibilities
P(at least one 3)= 11 36

3. Using a Tree Diagram
Suppose you are going to travel on a river. There are 2 choices for boats-- a kayak and a rowboat. There are three streams to follow-- north, northwest, and northeast.
6 possible outcomes.
What is the probability of taking a kayak directly north?
1 6

4. Counting Principle When rolling 2 dice we had 36 possible outcomes
6 choices for the 1st die and 6 for the 2nd.
Notice that 6×6 = 36, the size of the sample space
When choosing a river trip we had 6 possible outcomes
2 choices for a boat and 3 for direction
Notice that 2×3 = 6, the size of the sample space
So, the counting principle says that if there are 𝑚 ways of making a first choice and 𝑛 ways to make a second choice, then there are 𝑚×𝑛 ways to make both choices.

5. Practice
How many different sandwiches can you order when you choose one bread and one meat from the menu?
5 bread choices
6 meat choices
5×6=30 sandwich choices
If chicken is added to list of meats on the
menu, how many sandwiches are now
available? 35

6. Assignment
Odds
P.321 #11-27