Question

MATH399 Applied Managerial Statistics

Week 3 Assignment Diagrams for Probability

QuestionA survey on the spending habits of a sample of
households finds that two of the most common monthly expenses for
households in the sample are mortgages (home loans) and car loans.
The findings from the survey are presented in the Venn diagram
below.

A Venn diagram with an unlabeled universal set contains
two intersecting circles labeled Mortgages and Car loans that
divides the universal set into four regions labeled as follows,
where the label is given first and the content is given second:
Mortgages only, 11; Mortgages and Car loans only, 85; Car loans
only 24; outside the circles only, 9.

Given that a random household from the sample does not have a
mortgage, what is the probability that the household has a car
loan?

Provide the final answer as a simplified fraction.

QuestionA group of high school students reports who has a job
and who plays sports. The information is presented in the following
Venn diagram.

A Venn diagram with universal set contains two intersecting
circles labeled Job and Sports that divide the universal set into
four regions labeled as follows, where the region is given first
and the content is given second: Job only, 20; Job and Sports only,
8; Sports only, 16; Outside the circles only, 24.

Given that a random student has a job, what is the
probability that the student does not play sports?

•
Provide the final answer as a fraction.

QuestionThe probability that a debt holder has student loan
debt, given that they also have credit card debt is 2242. If we
know that 33 people in a sample of debt holders have student loan
debt and 42 people have credit card debt, fill in the Venn diagram
below with the number of debt holders to reflect this probability.

Let Event A represent the people with student loans, and
Event B represent the people with credit card debt.

QuestionThe probability that a person catches the flu given
that they’ve had a flu shot is 824. If we know that 36people caught
the flu and 24 people received flu shots, fill in the Venn diagram
below with the number of people to reflect this probability.

Let Event A represent those who received a flu shot, and
Event B represent those who caught the flu.

QuestionThe probability that a person who is trying to lose
weight exercises regularly, given that they are also on a diet is
515. If we know that 25 people who exercise regularly and 15 people
who are on a diet are all trying to lose weight, fill in the Venn
diagram below with the number of people to reflect this
probability.

Let Event A represent the people who exercise regularly, and
Event B represent the people who diet.

QuestionThe probability that a high school athlete is offered
admissions to a college, given that they were also involved in
music, is 715. If we know that 25 athletes and 15 musicians were
offered admission, fill in the Venn diagram below with the number
of students to reflect this probability.

Let Event A represent the athletes offered admission, and
Event B represent the musicians offered admission.

QuestionThe following Venn diagram shows the percent of
people who own a cat and own a dog.

A Venn diagram with an unlabeled universal set contains
two intersecting circles labeled Has a dog and Has a cat that
divide the universal set into four regions labeled as follows,
where the label is given first and the content is given second: Has
a dog only, 35 percent; Has a dog and has a cat only, 10 percent;
Has a cat only, 15 percent; outside the circles only, 40 percent.

Given that a randomly selected person has a cat, what is the
probability that the person also has a dog?

Give your answer as a decimal without any percent signs.
Round to two decimal places.

Venn Diagrams for Probability

QuestionGiven that a student takes algebra, what is the
probability that the student does not take chemistry?

Give your answer as a fraction. You may reduce it if you
want, but it is not necessary.

Key Terms

•
Venn Diagram: a picture that represents the outcomes of an
experiment, generally consisting of a box that represents the
sample space together with circles or ovals to represent events

QuestionA class of eighth graders reports who plays music and
who plays sports. They present the information in the following
Venn diagram.

A normal curve is over a horizontal axis and is
centered on 0.00. Two points are labeled on the horizontal axis,
one at negative 0.76 and another at 0.76. The area under the curve
to the left of negative 0.76 and right of 0.76 is shaded.

Given that a random student does not play music, what is the
probability that the student does not play sports?

•Provide the final answer as a fraction.

QuestionA survey of a sample of recent hires at major tech
companies aims to investigate which applicants are most likely to
be hired for positions in data science. The findings of the survey
are presented in the Venn diagram below.

A Venn diagram with an unlabeled universal set contains
two intersecting circles labeled Graduate degree and 10+ years
experience that divides the universal set into four regions labeled
as follows, where the label is given first and the content is given
second: Graduate degree only, 16; Graduate degree and 10+ years
experience only, 4; 10+ years experience only 20; outside the
circles only, 7.

Given that a random data scientist from the sample has
less than ten years of experience in the industry, what is the
probability that they have a graduate degree in a relevant
discipline?

Provide the final answer as a simplified fraction.

QuestionA fish fry is offering two types of fish tonight:
Halibut (H) and Tilapia (T). Halibut is offered only one way, and
the tilapia is offered four ways. A married couple eats dinner at
the fish fry, and each person orders a single fish option. The tree
diagram below shows the probabilities of the different outcomes.

A tree diagram has a root that splits into 2 branches
labeled H and T. Each primary branch splits into 2 secondary
branches, labeled H and T. Each branch has the following
probability: H, StartFraction 1 Over 5 EndFraction; T,
StartFraction 4 Over 5 EndFraction; H H, StartFraction 1 Over 5
EndFraction; H T, StartFraction 4 Over 5 EndFraction; T H,
StartFraction 1 Over 5 EndFraction; T T, StartFraction 4 Over 5
EndFraction.

Use the diagram to find the probability of the married couple
ordering both tilapia and halibut.

•
Provide the final answer as a fraction.

QuestionA newly minted coin is reportedly biased towards
tails. To find out whether this is true, the alleged unfair
coin is flipped twice. The tree diagram below shows the
probabilities of the different outcomes.

A tree diagram has a root that splits into 2 branches
labeled H and T. Each primary branch splits into 2 secondary
branches, labeled H and T. Each branch has the following
probability: H, StartFraction 1 Over 5 EndFraction; T,
StartFraction 4 Over 5 EndFraction; H H, StartFraction 1 Over 5
EndFraction; H T, StartFraction 4 Over 5 EndFraction; T H,
StartFraction 1 Over 5 EndFraction; T T, StartFraction 4 Over 5
EndFraction.

Use the diagram to find the probability of getting two tails
in a row.

•
Provide the final answer as a fraction.

QuestionProfessor Owen asked students to bend a coin with
pliers in order to create an unfair coin and observe the results of
flipping it multiple times. A student, Mary, bent a coin and
flipped the unfair coin twice in the air. The tree diagram below
shows the probabilities of the different outcomes.

A tree diagram has a root that splits into 2 branches labeled
H and T. Each primary branch splits into 2 secondary branches,
labeled H and T. Each branch has the following probability: H,
StartFraction 3 over 5 EndFraction; T, StartFraction 2 over 5
EndFraction; H H, StartFraction 3 over 5 EndFraction; H T,
StartFraction 2 over 5 EndFraction; T H, StartFraction 3 over 5
EndFraction; T T, StartFraction 2 over 5 EndFraction.

Use the diagram to find the probability of getting two heads
in a row.

•
Provide the final answer as a fraction.

QuestionA local chef was given the opportunity to demonstrate
two recipes at a food festival. She could not decide what to
select, so she flipped an unfair coin twice. A heads would mean
demonstrating an appetizer, and a tails would mean demonstrating an
entrée. The tree diagram below shows the probabilities of the
different outcomes.

A tree diagram has a root that splits into 2 branches
labeled H and T. Each primary branch splits into 2 secondary
branches, labeled H and T. Each branch has the following
probability: H, StartFraction 2 Over 7 EndFraction; T,
StartFraction 5 Over 7 EndFraction; H H, StartFraction 2 Over 7
EndFraction; H T, StartFraction 5 Over 7 EndFraction; T H,
StartFraction 2 Over 7 EndFraction; T T, StartFraction 5 Over 7
EndFraction.

Use the diagram to find the probability of the chef
demonstrating two entrées.

•
Provide the final answer as a fraction.

QuestionA survey on the educational backgrounds of a sample
of working computer scientists produces the findings presented in
the Venn diagram below.

A Venn diagram with an unlabeled universal set
contains two intersecting circles labeled Computer science and
Mathematics that divides the universal set into four regions
labeled as follows, where the label is given first and the content
is given second: Computer science only, 65; Computer science and
Mathematics only, 10; Mathematics only 13; outside the
circles only, 42.

Given that a random computer scientist from the sample does
not have a degree in computer science, what is the probability that
they do not have a degree in mathematics?

Provide the final answer as a simplified fraction.

QuestionThe probability that a person uses public transit
given that they also own a car is 814. If we know that 32 people in
a sample use public transit and 14 people own cars, fill in the
Venn diagram below with the number of people to reflect this
probability.

Let Event A represent the people who use public transit, and
Event B represent the people who own cars.

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