Finding Theoretical Probability Using an Area Model We

Finding Theoretical Probability Using an Area Model We are learning to…find theoretical probability of an event. Saturday, November 28, 2020

Reflection ¡ In complete sentences. Explain the different between experimental probability and theoretical probability. l 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 #1 Chris is rolling two number cubes and then finding the sum of the two results. What is theoretical probability that he will have a sum greater than or equal to 5? Number Cube #1 Area Model: Total Number of Outcomes: 36 Total Outcomes 1 2 What is 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

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 theoretical probability that she will flip heads and then spin a blue or a green on the spinner? Area Model: Coin Heads Tails Red Blue Total Number of Outcomes: 8 Total Outcomes What is theoretical probability that she will flip heads and then spin a blue or a green on the Green Yellow spinner? Spinner

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

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