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Math Problems
Precalculus
Combinations and permutations
Consider the following data set.
\newline
\begin{tabular}{|c|c|}
\newline
\hline Day of Month,
x
x
x
& Credit Card Balance,
y
y
y
\\
\newline
\hline
5
5
5
&
1864
1864
1864
\\
\newline
\hline
12
12
12
&
2298
2298
2298
\\
\newline
\hline
18
18
18
&
2706
2706
2706
\\
\newline
\hline
23
23
23
&
3043
3043
3043
\\
\newline
\hline
28
28
28
&
3385
3385
3385
\\
\newline
\hline
30
30
30
&
3519
3519
3519
\\
\newline
\hline
\newline
\end{tabular}
\newline
Use technology to find the Pearson correlation coefficient,
r
r
r
. Round your answer to two decimal places.
\newline
Enter the equation for the line of regression in the form
y
=
a
+
b
x
y=a+b x
y
=
a
+
b
x
where
a
a
a
and
b
b
b
are rounded to two decimal places.
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As Student Council President, Mona organized a school-wide scavenger hunt. She hid
8
8
8
goody bags,
5
5
5
of which were hidden in the computer lab. If
4
4
4
goody bags were randomly discovered during first period, what is the probability that all of them were hidden in the computer lab?
\newline
Write your answer as a decimal rounded to four decimal places._________
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Jen teaches a ceramics class on the weekends. In Sunday's class, the students created
9
9
9
clay objects,
7
7
7
of which were picture frames. After each class, Jen bakes the clay objects in a hot kiln to harden them. Students pick up their finished pieces later in the week.
\newline
If Jen randomly chose
6
6
6
clay objects to bake in the kiln Sunday night, what is the probability that all of them are picture frames?
\newline
Write your answer as a decimal rounded to four decimal places._________
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Over the past year, the chef at a popular restaurant has featured
8
8
8
different entrées,
6
6
6
of which are soups. If the chef creates a new menu by randomly selecting
4
4
4
previously featured entrées, what is the probability that all of them are soups?
\newline
Write your answer as a decimal rounded to four decimal places._________.
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A comedy club hosts an amateur comedy night, a good opportunity for aspiring comedians to perform. Of the
9
9
9
amateur comedians who signed up for tonight's show,
7
7
7
perform farcical comedy. If the host randomly selects
6
6
6
comedians from the sign-up list, what is the probability that all of them practice farcical? Write your answer as a decimal rounded to four decimal places.._________
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Joey volunteers at a children's hospital as an Art Director. He brought
8
8
8
T-shirts for the children to decorate this week.
5
5
5
of the T-shirts are a size small. If Joey was in a rush to get to the hospital, and he randomly grabbed
4
4
4
T-shirts to decorate, what is the probability that all of them are small? Write your answer as a decimal rounded to four decimal places.._________
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Scott got a summer job at a movie theater cleaning the aisles after each film. This Sunday,
8
8
8
movies are scheduled to show,
5
5
5
of which feature a teenager as the one main protagonist. If Scott is randomly assigned to clean up after
4
4
4
movies, what is the probability that all of them feature a teenager as the one main protagonist? Write your answer as a decimal rounded to four decimal places.._________
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Cora organized a technology career fair at her high school. She did an excellent job recruiting
8
8
8
guest speakers,
5
5
5
of whom worked in construction technology.
\newline
If Cora randomly assigns
4
4
4
speakers to speak during the afternoon session, what is the probability that all of them work in construction technology?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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Malia is shopping for a costume at a thrift store. There are
8
8
8
costumes hanging on the rack, including
6
6
6
witch costumes.
\newline
If the costumes all look like the right size, and Malia randomly selects
4
4
4
to try on, what is the probability that all of them are witch costumes?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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There are
8
8
8
students performing in the talent show,
5
5
5
of whom will juggle.
\newline
If
4
4
4
students are randomly chosen to perform during the first section of the show, what is the probability that all of them will juggle?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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Adriana and her best friend wanted to paint their apartment. In their storage closet, they found
9
9
9
cans of paint. Adriana remembered that
7
7
7
of the cans contained light blue paint, but none of the cans had labels.
\newline
If Adriana randomly opened
6
6
6
cans, what is the probability that all of them contain light blue paint?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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Matt and some of his friends are going rock climbing this weekend. In preparation, Matt purchased
8
8
8
sports drinks to bring, including
6
6
6
strawberry flavored drinks.
\newline
If Matt randomly chooses to place
5
5
5
drinks in the red cooler, what is the probability that all of them are strawberry flavored?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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During her semester living abroad, Cindy made a list of famous buildings to visit. Of the
7
7
7
buildings on her list,
5
5
5
were examples of Gothic architecture.
\newline
If Cindy randomly chose
4
4
4
buildings to visit during the first half of the semester, what is the probability that all of them are examples of Gothic architecture?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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Tony and Whitney made a list of
9
9
9
psychology experiments they want to try at home. Each experiment tackles one specific psychology topic.
7
7
7
of the experiments involve music and memory.
\newline
If Tony and Whitney randomly choose
6
6
6
experiments to try over the summer, what is the probability that all of them involve music and memory?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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There are
7
7
7
students performing in the talent show,
5
5
5
of whom will juggle.
\newline
If
4
4
4
students are randomly chosen to perform during the first section of the show, what is the probability that all of them will juggle?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the
7
7
7
total articles submitted,
5
5
5
were editorials. If she liked all the articles equally, and randomly selected
4
4
4
articles to go on the front cover, what is the probability that all of them are editorials? Write your answer as a decimal rounded to four decimal places. ____
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Evan brought
7
7
7
bagels to school,
5
5
5
of which are blueberry.
\newline
If Evan randomly gives away
4
4
4
bagels to teachers, what is the probability that all of them are blueberry?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
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Jim is shopping for a costume at a thrift store. There are
8
8
8
costumes hanging on the rack, including
6
6
6
superhero costumes.
\newline
If the costumes all look like the right size, and Jim randomly selects
5
5
5
to try on, what is the probability that all of them are superhero costumes?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
\newline
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Sanjay is helping his younger brother wrap presents for the holidays. They have
8
8
8
different rolls of wrapping paper, including
6
6
6
rolls with a comic strip design.
\newline
If Sanjay's brother randomly chooses
5
5
5
rolls of wrapping paper to wrap the first group of presents, what is the probability that all of them have a comic strip design?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
____
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Debbie and some of her friends are going rock climbing this weekend. In preparation, Debbie purchased
8
8
8
sports drinks to bring, including
6
6
6
lime flavored drinks. If Debbie randomly chooses to place
4
4
4
drinks in the red cooler, what is the probability that all of them are lime flavored? Write your answer as a decimal rounded to four decimal places. ____
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There are
13
13
13
college students running for student government class president. The candidates include
5
5
5
biology majors.
\newline
If
9
9
9
of the candidates are randomly chosen to give the first
9
9
9
speeches, what is the probability that exactly
2
2
2
of the chosen candidates are biology majors?
\newline
Write your answer as a decimal rounded to four decimal places.
\newline
□
\square
□
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