07 Jan A Venn diagram with

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.