DEVRY MATH399 Week 3 Assignment Diagrams for Probability Latest 2019 JULY Question # 00603577 Subject: Mathematics Due on: 08/10/2019 Posted On: 08/10/2019 06:21 AM Tutorials: 1 Rating: 5.0/5

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.