Name: __________________________________
AP Statistics
Simulation #1
Simulation: the imitation of chance behavior, based on a model that accurately reflects the experiment under
consideration
Parts of a simulation model:
 State the model, defining the key components
 State what one trial would be, including a stopping rule if necessary
 State what you would record
 State assumption (optional for AP Exam)
 Conduct the trials and record observations (AP Exam requires you to use a random digit table)
 Summarize and draw conclusion (only appropriate to do if you have at least 100 trials)
Suppose that we wanted to know the following:
“On average, how many girls would you expect in a family of three children?”
1) How could we collect data to answer this question?
2) How easy/difficult would it be to gather this information?
3) What is the probability that a child will be male versus female?
4) What random chance occurrence has the same probability as gender of a child?
In groups of three or four, perform a simulation to answer the question above. Use the following to help you
carry out the simulation.

State the model, defining the key components
What random chance occurrence will you use to represent gender? Define what will constitute a girl and
what will constitute a boy.

State what one trial would be, including a stopping rule if necessary
What will represent one family?

State what you would record
What information about the family are you interested in knowing?

Conduct the trials and record observations
Conduct 100 trials of your simulation.
Trial #
Trial #
Trial #
Trial #
Trail #
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Draw a histogram for these data. What variable should be on the horizontal axis? (Remember this is discrete
data, so center the bars over the x-values.)

Summarize and draw conclusion
Using the data above, on average, how many girls would you expect in a family of three children?
Now explain how you could use a random digit table (like the partial one below) to simulate this problem.
Carry out 3 trials, marking on the random digit table. Record your results.
7 1 0 3 5 0 9 0 0 1 4 3 3 6 7 4 9 4 9 7 7 2 7 1 9 9 6 7 5 8
2 7 6 1 1 9 1 5 9 6 5 4 5 8 0 8 1 5 0 7 2 7 1 0 2 5 6 0 2 7
Trial#
1
2
3
Homework:
Describe a simulation for the each of following questions. Perform three trials and record your results. DO
NOT answer the question.
1) A newly married couple agrees that they want to have children. The husband wants to have at least one son,
and the wife wants to have at least one daughter. They are interested in finding how many children they can
expect to have before having at least one boy and one girl.
1 9 2 2 3 9 5 0 3 4 0 5 7 5 6 2 8 7 1 3 9 6 4 0 9 1 2 5 3 1 4 2 5 4 4 8 2 8 5 3 7 3 6 7
6 4 7 1 5 0 9 9 4 0 0 0 1 9 2 7 2 7 7 5 4 4 2 6 4 8 8 2 4 2 5 3 6 2 9 0 4 5 4 6 7 7 1 7
09 7 7 5 5 8 0 0 0 9 5 3 2 8 6 3 2 9 4 8 5 8 2 2 2 6 9 0 0 5 6 5 2 7 1 1 3 8 8 8 9 9 3
2) Ralph did not study for the statistic quiz, so he guessed on the ten multiple-choice questions (four answer
choices). What is the estimated probability that he passed the quiz?
9 5 8 5 7 0 7 1 1 8 8 7 6 6 4 9 2 0 9 9 5 8 8 0 6 6 5 6 9 7 9 9 8 6 2 4 8 4 8 2 6
0 3 2 5 3 3 0 4 4 7 0 2 9 6 6 9 8 4 4 0 7 9 0 7 8 5 6 5 9 5 6 8 6 3 8 2 3 8 1 6
3 2 6 2 1 8 3 7 0 6 3 2 2 3 4 1 7 2 6 1 8 5 4 1 4 4 8 7 5 5 3 2 7 9 85 7 3 1 9
3) Estimate the number of times you expect to roll a die before one side appears twice.
6 9 0 5 1 6 4 8 1 7 8 7 1 7 4 0 9 5 1 7 8 4 5 3 4 0 6 4 8 9 8 7 2 0 1 9 7 2 4 5 3 6 7 5
9 5 8 9 8 4 6 8 2 8 8 2 2 9 1 3 1 8 6 3 8 5 4 3 0 3 0 0 7 9 5 0 8 7 2 7 1 5 6 8 9 1 4 2
2 7 0 6 5 6 5 1 4 3 7 4 1 3 3 5 2 4 9 3 6 7 8 1 9 8 2 8 7 2 0 9 4 3 9 0 9 9 9 4 7 7 2 5