Tree Diagram and Fundamental Counting Principle

Sample Spaces, Tree Diagrams & The Counting Principle

​By the end of class, I will be able to understanding sample space and counting principle

What is a sample space?

• The collection of ALL possible outcomes in an "experiment" or "event"

• Used to find the probability of an event occuring.

Multiple Choice

How many outcomes are there for flipping a coin?

• 1

• 2

Multiple Choice

How many outcomes are there for flipping 2 coins?

• 1

• 2

• 3

• 4

How many outcomes are there?

• Heads, Heads

• Heads, Tails

• Tails, Heads

• Tails, Tails

• There are a total of 4 outcomes when flipping 2 coins.

Multiple Choice

What is the probability of getting 2 tails?

• 1/4

• 2/4

• 3/4

• 4/4

Multiple Choice

What is the probability of getting a heads AND a tails?

• 1/4

• 2/4

• 3/4

• 4/4

How many total possible outcomes for this spinner?

Fill in the Blank

What is the probability of spinning two of the same color?

Fill in the Blank

What is the probability of spinning a red AND a blue?

/

Tree Diagram

• Can be used to show a sample space

• Each "branch" of the diagram represents one possible outcome

Multiple Choice

What is the probability of making both shots?

• 1/4

• 2/4

• 3/4

• 4/4

The Counting Principle

• Easier way to find a sample space

• Helpful for a large number of outcomes/event

• multiply the number of possible outcomes for EACH "event"

You have 4 different pairs of socks and 6 different pairs of sneakers. How many different combinations of socks and shoes do you have?

• 4 socks

• 6 sneakers

• 4x6=24 combinations

Fill in the Blank

At Joey's Italian Restaurant, there are 6 choices for appetizers and 8 choices for entrees. How many different appetizer and entree choices are there?

Fill in the Blank

The Dough Hut doughnut shop has 2 different types of doughnuts, 5 different types of icing and 4 different toppings. If each doughnut has one type of icing and one type of topping on it, how many doughnut varieties are there?