# Finding Theoretical Probability Using an Area Model

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Finding Theoretical Probability Using an Area Model
We are learning to…find the theoretical probability of an event.

Warm-Up --- February 28 Reflection (on a half sheet of paper)
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.

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

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 RH BH GH YH RT BT GT YT Heads Coin Tails Red Blue Green Yellow Spinner

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

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

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