We are given that this quarter Todd earned As in his classes 45 % of the time. Let's design and conduct a simulation to estimate the probability that Todd will earn an A in his next class. First let's review the steps for designing a simulation.
Choose and describe an appropriate probability model for the situation.
Define a trial for the situation and choose the number of trials to be conducted.
We will follow these steps, conduct the simulation, and report the results.
Designing a Simulation
Since we are interested in the probability that Todd will earn an A, we have two possible outcomes — earning an A and not earning an A. Based on the given information, we will assume that the theoretical probability that Todd will earn an A is 45 %.
Possible Outcomes
Theoretical Probability
Earning an A
45 %
Not Earning an A
(100- 45) % or 55 %
We will also assume that Todd will take the next class. Since we are asked to use a geometric probability model, we can use a spinner divided into two sectors — each sector representing one of the probabilities. Let's calculate the measure of the central angle of each sector.
Possible Outcomes
Measure of the Central Angle
Earning an A
45 %* 360^(∘)=162^(∘)
Not Earning an A
55 %*360^(∘)=198^(∘)
Now we are ready to create our spinner. Each trial — one spin of the spinner — will represent the result of one of Todd's classes.
Let's choose the number of trials to be 20. A successful trial in this case is landing on the area that represents earning an A.
Conducting and Summarizing Data from a Simulation
Now we can conduct a simulation. To do this let's spin our spinner 20 times.
Using the results from the table, we can calculate the experimental probability P that Todd will earn an A.
P=8/20=0.4
The experimental probability that Todd will earn an A is 0.4, or 40 %. Therefore, the experimental probability that they will not earn an A is 1-0.4=0.6, or 60 %. Finally, we can create a bar graph showing these results.
Notice that this is only an example solution, as we can think of many other simulations we can design and conduct using the given information.
