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

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

Reflection (on white boards!!!)  In complete sentences. Explain the different between experimental probability and theoretical probability. Provide Examples! Raise your board in the air when you are done!!!

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? Area Model: Total Number of Outcomes: What is the theoretical probability that he will have a sum greater than or equal to 5? N u m b e r C u b e # 1 Number Cube #2 1 2 3 6 5 4 1 2 3 6 5 4 7 89 1011 12 6 7 8 9 10 11 5 6 7 8 9 10 5 6 7 8 9 5 6 7 8 5 6 7 36 Total Outcomes

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? Coin Spinner 8 Total Outcomes RH BH GH YH RT BT GT YT Heads Tails Red Blue Yellow Green Blue Yellow Red Green

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? Spinner Number Cube 5 20 15 10 1 2 3 6 5 4 24 Total Outcomes 5 10 1520

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

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