Download A Gaggle of Girls

A Gaggle of Girls
The Weavers have 3 children: Sarah, Gail, and Christine. If we assume that a
couple is equally likely to have a girl or a boy, then how unusual is it for a family
like the Weavers to have 3 children who are all girls?
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If success = girl, and boy = failure, then the probability of success is 0.5.
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We will define the random variable “X” as the number of girls.
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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 what is
P(X = 3)??
Tactile
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Using a coin, let “heads” represent “girl” and “tails” represent “boy”.
One trial = Flip the coin three times and make note of the outcome of
each flip.
Example: {heads, heads, tails} is one trial that represents a family of three
with a {girl, girl, and boy}.
Record the outcome of each trial below.
Complete 35 trials.
2. Use tally marks in the table below to record (keep track of) your
results.
3 Girls
Not 3 Girls
3. From your trials, what is the relative frequency of P(X = 3)?
Graphing Calculator
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Using the codes 1 = girl and 0 = boy, enter the command “randInt(0, 1, 3)”.
This command instructs the calculator to randomly pick a whole number
from the set {0, 1}
One trial = use the above command and hit enter.
The outcome {0, 0, 1}, using the codes, means {boy, boy, girl}, in that order.
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Continue to press ENTER and count “success” and “failure” for a family
of 3 children (keep track of this below)
Complete 35 trials.
5. Use a tally mark to record each time you observe a success {1, 1, 1} result.
3 Girls
Not 3 Girls
6. From your trials, calculate the relative frequency for the event P(X = 3).
Using Probability
Determine the total number of outcomes for this experiment.
7. List the outcomes in the sample space. (Ex: BBB,…)
8. From the sample space, complete the probability distribution table for the
random variable X = number of girls.
X=
0
1
2
3
P(X) =
Using the Binomial Distribution Methods
9. Using the calculator binomial feature, complete the probability
distribution table for the random variable X = number of girls.
X=
P(X) =
0
1
2
3
10. In order to obtain the answer for P(0), what did you type in your
calculator?
11. Do the results of your simulations come close to the theoretical value
for P(X = 3)? Why or why not?