From the following list of hypothetical situations, identify those that are independent events using the given probabilitiesof each event and the formal definition of independence.In a college course survey, 20% of students received an A in chemistry, 25% of students received an A in biology,and 5% of students received an A in both chemistry and biology.At a particular university, 12% of students were in a doctorate program, 16% of students were engineering majors,and 3% of students were in a doctorate program and were engineering majors.In a yearly weather survey of a city, 32% of the days had precipitation, 25% of the days were weekend days, and 8%of the days had precipitation and were weekend days.In a study of color blindness, 10% of the individuals were color-blind, 52% of the individuals were male, and 8% ofthe individuals were color-blind and were male.

Independent Condition P(A∩B) = P(A).P(B)

Answered: From the following list of hypothetical…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Here are three lotteries played by three individuals that cost $100. Could you tell whether they are risk-neutral, risk-seeking(loving) or risk-averse? the percentages in () are the probabilities associated with the events. 1)Win (50%): gets $180, lose (50%): gets $40; 2)Win (50%): gets $160, lose (50%): $0; 3)Win (20%): gets $300, lose (80%): gets $50. which one of these individuals are more likely to pursue entrepreneurship? Briefly explain why.
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (8), and an automatic transmission (C). If 46% of all purchasers request A, 57% request 8, 76% request C, 71% request A or 8, 89% request A or C, 88% request 8 or C, and 94% request A or 8 or C, determine the probabilities of the following events. [Hint: "A or 8" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. 0.85 X (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.
A manufacturing plant produces light bulbs in three different colors: red, blue, and green. The probabilities of producing a red, blue, or green bulb are 0.2, 0.5, and 0.3, respectively. If a customer buys six bulbs at random, what is the probability of receiving at least two bulbs of each color?
Consider two events following receiving a bachelor’s degree from a prestigious university: A = {being accepted into a graduate program} and B = {receiving a job offer}. We know the following is true: P(A) = P(B) = 0.7 P(A|B) = 0.9 Are events A and B independent? Why or why not?
In a large university, 60% of students play sports, 30% are involved in the arts, and 10% participate in neither activity. Among the sport-playing students, 70% play team sports, and 30% play individual sports. Additionally, 40% of the art-involved students are focused on visual arts, and 60% on performing arts. If a random sample of 200 students is taken from the university, what is the probability that exactly 84 students play team sports, 36 play individual sports, 48 are involved in performing arts, 24 in visual arts, and 8 students participate in neither sports nor arts?
At the Washington University 35%, 25% and 40% of the students in Calculus are taught by Prof. A, Prof. B and Prof. C, respectively. The respective probabilities of failing in Calculus for the three professors are 6%, 7% and 5%. A student in Calculus in the previous semester was randomly selected and was found out to have failed in the subject. Under which class most likely did he belong?
A retailer of automobile parts has four employees, K, L, M, and N, who make mistakes in filling an order one time in 100, four times in 100, two times in 100, and six times in 100. Of all the orders filled, K , L, M, and N fill, respectively, 20%, 40%, 30%, and 10%. If a mistake is found in a particular order, what are the probabilities that it was filled by K, L, M, or N?
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 36% of all purchasers request A, 47% request B, 69% request C, 54% request A or B, 75% request A or C, 76% request B or C, and 78% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.
From a large survey of customers using a chain of coffee shops, 60% of the customers are male, 50% purchase food, 15% are both Male and purchase food. What are the probabilities that: A customer is both female and purchases food? A female customer purchases food? A customer purchasing food is female?
On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process
A market survey shows that 60% of the population used Brand X laundry detergent last year, 7% of the population gave up doing its laundry last year, and 6% of the population used Brand X and then gave up doing laundry last year. Are the events of using Brand X and giving up doing laundry independent? O Yes O No Is a user of Brand X detergent more or less likely to give up doing laundry than a randomly chosen person? O A user of Brand X laundry detergent is as likely to quit doing laundry as a randomly chosen person. O A user of Brand X laundry detergent is less likely to quit doing laundry than a randomly chosen person. O A user of Brand X laundry detergent is more likely to quit doing laundry than a randomly chosen person.

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