Sample Space and Fundamental Counting Principle

Sample Spaces, Tree Diagrams & The Counting Principle

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What is a sample space?

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

• Is 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 outcomes for this spinner?

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

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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

• 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 Blanks

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 Blanks

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?