Follow the steps for designing a simulation using random number generators.
See solution.
Practice makes perfect
We are given survey results about sports that high school athletes play. Let's design and conduct a simulation to estimate the probability that an athlete will play each of these sports. We will first 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 an athlete will play each of the given sports, we will choose out of 4 disciplines. Therefore, we have 4 possible outcomes. We will assume that the theoretical probability that a random person will choose each of these sports is the same as the given percentages.
Possible Outcomes
Theoretical Probability
Written as Fraction
Volleyball
15 %
3/20
Soccer
20 %
4/20
Basketball
30 %
6/20
Football
35 %
7/20
Let's use a random number generator to perform the simulation. To do this, because we expressed the probabilities as fractions with denominators of 20, we will assign the integers from 1 to 20 to represent the probability data.
Volleyball:& 1,2,3
Soccer:& 4,5,6,7
Basketball:& 8,9,10,11,12,13
Football: & 14,15,16,17,18,19,20
Each trial — one generated number — will represent the sport of a random athlete. Let's choose the number of trials to be 20.
Conducting and Summarizing Data from a Simulation
We will use the random number generator in our graphing calculator. To do so, push the MATH button. Then scroll left to the PRB menu and choose the fifth option, randInt(.
After choosing this option, enter the minimum and maximum values of the set and the number of trials. Next, push ENTER.
Now we can make a frequency table to show the example results of our simulation. Remember the numbers that we assigned to represent each genre when keeping track of the outcomes.
Outcome
Tally
Frequency
Volleyball
||
2
Soccer
||||
4
Basketball
|||||
5
Football
||||| ||||
9
Total
-
20
Using the results from the table, we can calculate the experimental probability P of choosing each genre. We will divide the frequency of choosing each discipline by the number of trials, 20.
Outcome
Frequency
Probability P
Volleyball
2
2/20 or 10 %
Soccer
4
4/20 or 20 %
Basketball
5
5/20 or 25 %
Football
9
9/20 or 45 %
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.
