We know that Zoe struck out on 10 % of her at bats last season. We want to design and conduct a simulation to estimate the probability that she will strike out at her next at bat this season. 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 Zoe will strike out, we have two possible outcomes — striking out and not striking out. Based on the given information, we will assume that the theoretical probability that she strikes out is 10 %.
Possible Outcomes
Theoretical Probability
Striking out
10 %
Not striking out
(100- 10) % or 90 %
To design the experiment we will 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
Striking out
10 %* 360^(∘)=36^(∘)
Not striking out
90 %*360^(∘)=324^(∘)
Now we are ready to create our spinner. Each trial — one spin of the spinner — will represent the result of one of Zoe's at bats.
Let's choose the number of trials to be 20. A successful trial in this case is landing on the area that represents striking out.
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 Zoe will strike out at her next at bat.
P=3/20=0.15
The experimental probability that Zoe will strike out at her next at bat is 0.15, or 15 %. Therefore, the experimental probability that she will not strike out is 1-0.15=0.85, or 85 %. Finally, we can create a bar graph showing these results.
Keep in mind that this is just one of many simulations we could do.
