Finding Theoretical Probability Using an Area Model

1
Finding Theoretical Probability Using an Area
Model

• We are learning tofind the theoretical
  probability of an event.
• Wednesday, March 26, 2014

2
Reflection

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

3
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.

4
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?
Area Model Total Number of Outcomes
Area Model What is the theoretical probability that he will have a sum greater than or equal to 5?
1
36 Total Outcomes
2
3
Number Cube 1
4
5
6
2
6
5
4
1
3
Number Cube 2
5
Area Model Example 2
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
Area Model What is the theoretical probability that she will flip heads and then spin a blue or a green on the spinner?
8 Total Outcomes
Heads
Coin
Tails
Red
Yellow
Green
Blue
Spinner
6
Area Model Example 3
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
Area Model What is the probability that his result will be an even number?
24 Total Outcomes
5
10
Spinner
15
20
2
6
5
4
1
3
Number Cube
7
Reflection

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