Finding Theoretical Probability Using an Area Model

We are learning to…find the theoretical probability of an event.

Thursday, April 20, 2023

Reflection

In complete sentences. Explain the different between experimental probability and theoretical probability. Provide Examples!

Directions for using an Area Model:

Read the probability situation carefully and determine the two different events taking place.

Draw a rectangle. Assign and label one side (length or width) of the

rectangle one event and do the same for the other event. Divide the length and the width into equal sections based

on the number of outcomes for each of the two events. Count the squares created in the rectangle to find the

total number of outcomes (this will be the denominator of your fraction).

Color in all favorable outcomes. Count all favorable outcomes (this will be the numerator

of your fraction). Simplify the fraction if possible.

Area Model Example #1Chris is rolling two number cubes and then finding the sum of the two results. What is the theoretical probability that he will have a sum greater than or equal to 5?

Area Model: Total Number of Outcomes:

What is the theoretical probability that he will have a sum greater than or equal to

5?

Nu

mb

er

Cu

be #

1

Number Cube #2

1

2

3

6

5

4

1 2 3 654

36 Total Outcomes

30

36

5

6

Area Model Example #2Samantha is flipping a coin and then spinning a spinner with the colors red, blue, green and yellow. What is the theoretical probability that she will flip heads and then spin a blue or a green on the spinner?

Area Model: Total Number of Outcomes:

What is the theoretical probability that she will flip heads and then spin a blue or a green on the

spinner?

Coin

Spinner

8 Total Outcomes

2

8

1

4

Heads

Tails

Red Blue YellowGreen

Blue

Yellow

Red

Green

Area Model Example #3Ricky is rolling a number cube with the numbers 1-6 and then spinning a spinner with the numbers 5, 10, 15, 20. He then finds the sum of the number cube and spinner result. What is the probability that his result will be an even number?

Area Model: Total Number of Outcomes:

What is the probability that his result will be an

even number?

Sp

inn

er

Number Cube

5

20

15

10

1 2 3 654

24 Total Outcomes

12

24

1

2

5 10

15 20

Reflection

What are some possible advantages and disadvantages to finding theoretical probability with: Area Models Tree Diagrams