Transcript Mod 3 - Theoretical Probability - Area Model

Finding Theoretical Probability
Using an Area Model
We are learning to…find the theoretical
probability of an event by creating lists
and diagrams.
Thursday, June 2, 2016
Vocabulary
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Theoretical Probability - Probability that is
based on likelihood of an event happening
based on all the possible outcomes.
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When calculating Theoretical Probability
we will not perform the experiment.
Today we will represent and analyze all
possible outcomes of an event by
making an Area Model.
Directions for using an Area Model:
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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 #1
Chris 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?
Number Cube #1
Area Model:
Total Number of Outcomes:
1
36 Total Outcomes
2
What is the theoretical
probability that he will have
a sum greater than or equal
to 5?
3
4
5
6
1
2
3
4
5
6
Number Cube #2
30 5

36 6
Blue
Area Model Example #2
Yellow
Red
Green
Samantha 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:
8 Total Outcomes
Coin
Heads
What is the theoretical
probability that she will
flip heads and then spin
a blue or a green on the
spinner?
Tails
Red
Blue
Green Yellow
Spinner
1
2

4
8
Try the last question
with your team!
Area Model Example #3
5
10
15
20
Ricky 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:
24 Total Outcomes
Spinner
5
What is the probability
that his result will be an
even number?
10
15
20
1
2
3
4
5
Number Cube
6
12 1

24 2