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=====-Chapter
8 The Binomial and Geometric Distributions
I
ACTIVITY 8
A
Gaggle of Girls
The Ferrells have 3 children: Jennifer, Jessica, and Jaclyn. If we assume that a
couple is equally likely to have a girl or a boy, then how unusual is it for a fam-
ily like the Ferrells to have 3 children who are all girls? We have encountered
problems like this in an earlier chapter. But this time we're going to use the
method of simulation. If success
=
girl, and failure
=
boy, then p(success)
=
0.5. We will define the random variable X as the number of girls. Then we
want to simulate families with 3 children. Our goal is to determine the long-
term relative frequency of a family with 3 girls, that is, P(X
=
3).
1. Using a random number table, let even digits represent. "girl" and odd
digits represent "boy." Select a row, and beginning at that row, read off num-
bers 3 digits at a time. Each
3
digits will constitute one trial. Use tally marks
in a table like this one to record the results:
Do at least 40 trials. Then combine your results with those of other stu-
dents in the class to obtain at least 200 trials. Calculate the relative fre-
quency of the event (3 girls).
2. For variety, do the same thing as before, but this time using the calculator.
Using the codes 1
=
girl and 0
=
boy, enter the command
randInt
(
O,1,3
)
.
This command instructs the calculator to randomly pick a whole number from
the set (0, 1) and to do this 3 times. The outcome (0, 0,
l), using our codes,
means {boy, boy,
girl),
in that order. Continue to press -Nand
count until
you have 40 trials. Use a tally mark to record each time you observe a (1, 1, 1)
result. Calculate the relative frequency for the event (3 girls).
3.
Extra for programming
experts: Write a calculator program to carry out the
process described above. Allow the user to specify the number of trials, and have
the calculator report the relative frequency of (3 girls) as a decimal number.
1
4. Determine the total number of outcomes for this experiment. List the
1
outcomes in the sample space. Then complete the probability distribut'
table for the random variable
X
=
number of girls.
Do the results of your simulations come close to the theoretical value
for P(X
=
3)?