We are given that, on 80 % of her Biology quizzes in the first semester, Clara got an A. We want to design and conduct a simulation to estimate the probability that, in the second semester, she will get an A on another biology quiz. 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, then conduct the simulation, and report the results.
Designing a Simulation
Since we are interested in the probability that Clara will get an A, we have two possible outcomes — getting an A and getting any grade below an A. Based on the given information, we will assume that the theoretical probability that she will get an A is 80 %.
Possible Outcomes
Theoretical Probability
Getting an A
80 %
Getting any grade below an A
(100- 80) % or 20 %
We will also assume that Clara will take the quizzes in the second semester. Since we are asked to use a geometric 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
Getting an A
80 %* 360^(∘)=288^(∘)
Getting any grade below an A
20 %*360^(∘)=72^(∘)
Now we are ready to create our spinner. Each trial — one spin of the spinner — will represent the result of one of Clara's second semester quizzes.
Let's choose the number of trials to be 20. A successful trial in this case is landing on the area that represents getting 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 Clara will get an A.
P=14/20=0.7
The experimental probability that Clara will get an A on her second semester quizzes is 0.7 or 70 %. Therefore, the experimental probability that she will get a grade below an A is 1-0.7=0.3 or 30 %. Finally, we can create a bar graph showing these results.
