We are given that Max scores 35 % of the goals his team earns in each water polo match. Let's design a simulation to estimate the probability that, in the next polo match, Max will score a goal for his team. 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.
Let's follow these steps, one at a time.
Step 1
Since we are interested in the probability that Max will score a goal in the next match, we have two possible outcomes — Max scores a goal and Max does not score a goal. Based on the given information, we will assume that the theoretical probability that he will score a goal is 35 %.
Possible Outcomes
Theoretical Probability
Max Scores a Goal
35 %
Max Does Not Score a Goal
(100- 35) % or 65 %
Step 2
We will also assume that Max will play in the next water polo match. Otherwise, we would need to consider the conditional probability.
Step 3
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
Max Scores a Goal
35 %* 360^(∘)=126^(∘)
Max Does Not Score a Goal
65 %*360^(∘)=234^(∘)
Now we are ready to create our spinner. Each trial — one spin of the spinner — will represent the result of one of Max's games.
Step 4
Finally, let's choose the number of trials to be 50. A successful trial in this case is landing on the area that represents Max scoring a goal. The results of conducting the described simulation can be recorded in a frequency table and used to evaluate an experimental probability. Keep in mind that this is just one possible simulation we can create.
