Transcript Simulating Experiments

AP STATISTICS
LESSON 5 - 3
SIMULATING EXPERIMENTS
ESSENTIAL QUESTION:
How can simulation be used to solve
problems involving chance?
Objectives:
 To simulate problems of chance with the help of a
random number table.
 To simulate problems of chance using the
calculator.
Three methods of simulation to answer
questions involving chance.
1.
2.
3.
Try to estimate the likelihood of a result by
actually carrying out the experiment.
Develop a probability model and use it to
calculate a theoretical answer.
Start with a model that, in some fashion,
reflects the truth about the experiment, and
then develop a procedure for simulating of
repetitions of the experiment.
Simulation
The imitation of chance behavior, based on a model
that accurately reflects the experiment under
consideration, is called a simulation.
Independent (trials) – One event has no effect or
influence over the next (e.g. coin tosses).
Simulation Steps
Step 1: State the problem or describe the experiment.
Step 2: State the assumptions.
Step 3: Assign digits to represent outcomes.
Step 4: Simulate many repetitions.
Step 5: State your conclusions.
Simulation using the calculator or computer
 Using the calculator or statistical software to
estimate probability through simulation is faster
than doing it by hand.
Problem 5.67 Tennis Racquets
Professional tennis players bring multiple racquets to each match. They know that
high string tension, the force with which they hit the ball and occasional “racquet
abuse” are all reasons why racquets break during a match. Brian Lob’s coach tells
him that he has a 15% chance of breaking a racquet in any given match. How many
matches on average can Brian expect to play until he breaks the racquet and needs
to use a backup? Use simulation methods to answer the question.
 Step 1: State the problem or describe the experiment.

Brian has a 15% chance of breaking his racquet in any given match.
We want to know how many matches he can play until he breaks his
racquet.
 Step 2: State the assumptions:


We can assume that the racquet use in the matches is independent.
One match does not effect the other in terms of the racquet
We know that he has a 15% chance of breaking the racquet leaving a
85% chance of not breaking the racquet.
 Step 3: Assign digits to represent outcomes:


I will assign 00 to 14 to represent breaking the racquet
I will assign 15-99 to represent not breaking the racquet
Problem 5.67 Continued
 Step 4: Simulate many repetitions:



Using our calculator we can generate one number at a time to
decide how many matches it took Brian to break the racquet,
record that number, and then repeat the simulation.
RandInt(00,99,1)
We will repeat the simulation twice each and then compute the
average number of matches he will play before his racquet breaks.
 Step 5: State your conclusions:


We can conclude that Brian will play an average of
games
before he breaks the racquet and has to use his backup.
In chapter eight, we will actually Use probability models to
calculate the true number of matches Brian will play before he
breaks his racquet.
Class Activity (5.3 Simulating Experiments) Part 2
Use your calculator to simulate a couple’s having children until they have a girl or until they
have 4 children. Use the simulation to estimate the probability that they will have a girl among
their children.
 First of all, we still have to follow the steps of simulation.
A couple will have children until they have
 Step 1: State the problem or describe the experiment:
 Step 2: State the assumptions:
a girl or until they have four children.

We can assume that the observations are independent of each other (this means that the sex of one
child will not effect the sex of the next child). Also, a boy or girl is equally likely to occur.

Step 3: Assign digits to represent outcomes:
Let 0 represent a boy and 1 represent a girl.

Step 4: Simulate many repetitions:
Using randInt(0,1,4) we can simulate a couple’s having 4 children. We will do this 10 times each and
combine our results to estimate the probability.


Step 5: State your conclusions:
Taking the number of desired outcomes out of the total number of repetitions, we can compute the
probability of having a girl for this couple to be:
Estimated probability =
Now, using our calculator, we were able to do many more repetitions in a timely manor.
Therefore our probability is more accurate.