A survey of magazine subscribers showed that 45.6% rented a car during the past 12 months for business reasons, 56% rented a car during thepast 12 months for personal reasons, and 28% rented a car during the past 12 months for both business and personal reasons,(a) What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons?(b) What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?

According to the given information,The probability that a subscriber rented a car during the past 12…

Answered: A survey of magazine subscribers showed…

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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A person invests $3 in a market in which he may gain $1 with probability or may lose $1 with probability in a period independently. • What is the probability that the person ever goes broke? • What is the expected time periods to go broke?
The probability that a statistics graduate from a Canadian university gets a data science job is 0.6. Ten graduates applied for executive jobs. (a) What is the probability that exactly 3 will get jobs? (b) What is the probability that at least 2 will get a job?
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze. (a) What is the probability that among 16 randomly observed individuals exactly 8 do not cover their mouth when sneezing? (b) What is the probability that among 16 randomly observed individuals fewer than 4 do not cover their mouth when sneezing? (c) Would you be surprised if, after observing 16 individuals, fewer than half covered their mouth when sneezing? Why? (a) The probability that exactly 8 individuals do not cover their mouth is 0.19 (Round to four decimal places as needed.) (b) The probability that fewer than 4 individuals do not cover their mouth is 0.76. (Round to four decimal places as needed.) (c) Fewer than half of 16 individuals covering their mouth would not be surprising because the probability of observing fewer than half covering their…
A certain bridge in Cebu is being re-constructed. The civil engineers would like to consider the number of heavy-duty vehicles that pass through that certain bridge in re-designing. The industrial engineers are tasked to do the job in finding the probability that certain number of heavy-duty vehicles pass through the bridge in a specific period of time. The IEs collected the data below. The IE would like to know if queuing theory is applicable in simulating the number of heavy-duty vehicles that pass through the bridge. One condition of using queuing theory is that the data must be Poisson distributed. Test at 1% level of significance if the data is collected by the IE is Poisson distributed.
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.Suppose you sit on a bench in a mall and observe people's habits as they sneeze. (a) What is the probability that among 16 randomly observed individuals exactly 5 do not cover their mouth when sneezing? (b) What is the probability that among 16 randomly observed individuals fewer than 4 do not cover their mouth when sneezing? (c) Would you be surprised if, after observing 16 individuals, fewer than half covered their mouth when sneezing? Why? (a) The probability that exactly 5individuals do not cover their mouth is nothing. (Round to four decimal places as needed.) (b) The probability that fewer than 4 individuals do not cover their mouth is nothing. (Round to four decimal places as needed.)
(3) Protein scoring matrices, such as the BLOSUM family, are often characterized by their relative entropy Ei og ) lij Σ 9ij ij where qj is the implied joint probability distribution of letters i and j, and pi is the probability distribution of a single letter i. (a) What properties of the relative entropy make it useful for comparing scor- ing matrices? (b) What would be more appropriate for comparing extremely divergent pro- tein sequences, a scoring matrix with large relative entropy or small relative entropy?
Please show full work for better understanding
6. An actuary studying the insurance preferences of automobile owners makes the following conclusions: (i) An automobile owner is twice as likely to purchase collision coverage as disability coverage. (ii) The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage. (iii) The probability that an automobile owner purchases both collision and disability coverages is 0.15. (a)Calculate the probability that an automobile owner purchases neither collision nor disability coverage. (b) Calculate the probability that an automobile owner purchases only collision coverage.
The US Bureau of Labor Statistics publishes data on the benefits offered by small companies to their employees. Supposed 42% offer retirement plans, and 61% offer life insurance. Further, suppose that if they offer life insurance, the probability they also offer retirement plans is 0.54. (a) Find the probability they do offer life insurance and do not offer a retirement plan. (b) If they do not offer life insurance, what is the probability they offer a retirement plan? (c) Find the probability they offer exactly one of the benefits (not both).
Suppose 40% of the restaurants in a certain part of a town are in violation of the health code. A health inspector randomly selects six of the restaurants for inspection. (Round your answers to four decimal places.) (a) What is the probability that none of the restaurants are in violation of the health code?(b) What is the probability that one of the restaurants is in violation of the health code?(c) What is the probability that at least two of the restaurants are in violation of the health code?

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