Transcript Finding Theoretical Probability Using an Area Model

Finding Theoretical Probability
Using an Area Model
We are learning to…find the
theoretical probability of an event.
Get out your Probability homework
for Miss. Huffman to check.
Be working on your reflection as I check HW.
Warm-Up --- February 28
Reflection (on a half sheet of paper)

In complete sentences. Explain the
difference 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 square on your graph paper. 12 units x 12 units
Assign and label one side (length or width) of the square
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.
Label each of the squares created like you would a
punnett square.
Count the squares created in the rectangle to find the
total number of outcomes (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:
1
5
6
7
5
6
7
8
5
6
7
8
9
10
2
3
Total Number of Outcomes:
4
5
6
7
8
9
5
6
7
8
9
10 11
6
7
8
9
10 11 12
1
2
3
4
5
6
Number Cube #2
36 Total Outcomes
What is the theoretical
probability that he will have
a sum greater than or equal
to 5?
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:
Coin
8 Total Outcomes
Heads
RH
BH
GH
YH
Tails
RT
BT
GT
YT
Red
Blue
Green Yellow
Spinner
What is the theoretical
probability that she will
flip heads and then spin
a blue or a green on the
spinner?
1
2

4
8
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
What is the Probability of the Prize Bag?
Miss. Huffman puts 8 marbles into a prize bag, and
Alexus picks one at random. Since Alexus’ got two
A’s this week, 2 of the marbles are
red, and the rest are white.
If Alexus picks a red marble, she gets to reach into
Miss. Huffman’s bag of candy.
Today, Miss. Huffman is left with only two kinds of
candy Strawberry Blowpops and Apple Blowpops.
Miss Huffman has an equal number of each.
What is the probability that Alexus ends up with a
strawberry Blowpop after this whole ordeal?
Reflection

What are some possible advantages
and disadvantages to finding
theoretical probability with:


Area Models
Tree Diagrams