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 Blanks

Fill in the Blanks

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