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**Finding Theoretical Probability Using an Area Model**

We are learning to…find the theoretical probability of an event. Thursday, April 20, 2017

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

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**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.

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**Total Number of Outcomes:**

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: 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 1 2 3 4 5 6 Number Cube #2

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**Total Number of Outcomes:**

Blue Yellow Red Green 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: 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 Blue Green Yellow Spinner

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**Area Model Example #3 Spinner Number Cube**

5 10 15 20 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: What is the probability that his result will be an even number? 24 Total Outcomes 5 10 Spinner 15 20 1 2 3 4 5 6 Number Cube

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

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