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.

State each possible outcome and the corresponding theoretical probability.
Determine if there are any assumptions.
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	$80 % \cdot 36 0^{\circ} = 28 8^{\circ}$
Getting any grade below an A	$20 % \cdot 36 0^{\circ} = 7 2^{\circ}$

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.

Let's use a frequency table to present the example results.

Outcome	Tally	Frequency
A	$∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣$	$14$
below an A	$∣ ∣ ∣ ∣ ∣$	$6$
Total	-	$20$

Using the results from the table, we can calculate the experimental probability

P

that Clara will get an A.

P = \frac{1 4}{2 0} = 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.

Exercise