Transcript Simulating Experiments using the calculator or computer

Simulations using the calculator
or computer
AP STATISTICS
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.
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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
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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.
Step 1: State the problem or describe the experiment: A couple will have children until they
have a girl or until they have four children.
Step 2: State the assumptions:
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)
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 4: 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.