1. A firm rents out cars and operates from three locations - the Airport, the Beach and the City. Customersmay return vehicles to any of the three locations. The company estimates that the probability of a car beingreturned to each location is as follows:AirportCar returned toCar hired fromAirport BeachCity121314 1312 34 13H444AFBeachCityFigure 1: Table of car-hire data.0(a) A car is currently parked in the city. What is the probability that, after being hired three times, it endsup in the city? [2 marks](b) A car is parked at the airport. On average, how many times will it need to be hired until it is left in thecity? [2](c) The firm has been running for many years with a fleet of 25 cars, of which 10 are currently on hire. Howmany of the other cars would you expect to be parked at each of the three locations? Explain your answerclearly. [4](d) Due to a coding error an intern accidentally inverts the list of dates of hire for the last year (so the mostrecent hire now looks like the first hire and the first hire looks like the most recent). The intern says nothingand hopes nobody will notice, will they be caught? Justify your answer. [2]

a) To find the probability that a car parked in the city ends up in the city after being hired three…

Answered: 1. A firm rents out cars and operates…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the Divergence Theorem to find the flux of F(x, y, z) = (x³ – e³)i+ (y³ + sin z).j+ (z³ – cy)k across the surface of the solid bounded above by z = V4 – x2 – y? and below by the xy-plane with outward orientation. Hint: Use spherical coordinates. NOTE: Enter the exact answer. 96 ||
Department Sex Packaging shipping total Female 32 48 80 male 48 72 120 Total 80 120 200 A local mail-order catalog business employs 200 people in the packaging and shipping departments. The personnel department maintains the records shown in Table below. Questions have arisen whether there has been a tendency to place female workers in the packaging department instead of in the shipping department. Management feels that there is no relationship between being female and working in the packaging department. They feel that these two events are independent. If an employee is selected at random from the 200 total employees, what is the probability that the employee works for the packaging department? A) if the employee selected at random is male, what is the probability that he works for the shipping department? B) if the employee selected at random is male, what is the probability that he works for the packaging department? C) is the probability of being male…
A company buys microchips from three suppliers I, II and III. Supplier I has a record of providing microchips that contain 10% defective; supplier a defective rate of 5% and supplier III has a defective rate of 3%. Suppose 10%, 40% and 50% of the current supply came from suppliers I, II and III, respectively. If a randomly selected microchip is defective, what is the probability that it came from supplier II? Express your answer accurate to two decimal places. O 48 O..40 O something else O 44 O 41
1. Researchers are interested in the relationship between vaping and upper respiratory infections. Suppose that 15% of their population of interest has vaped in the past year and 25% have had an upper respiratory infection in the past year. In addition, they know that 10% have both vaped and had an upper respiratory infection in the past year. What percent of the population has neither vaped nor had an upper respiratory infection in the past year? b. What is the probability of having an upper respiratory infection in the past year given that the person has vaped in the past year? What is the complement of the event in part b)? Be sure to interpret this probability in the context of the problem. a. C. d. What is the probability of having an upper respiratory infection in the past year given that the person has not vaped in the past year? Are the two events independent? Be sure to justify your answer. Based on your calculations what can you conclude about the relationship between vaping…
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1) The question screenshot attached down below just need final answer.
9. A law firm employs three types of lawyers: junior lawyers, senior lawyers, and partners. During a given year, there is a 0.1 probability that a junior lawyer will be promoted to senior lawyer and a 0.05 probability that he or she will leave the firm. Also, there is a 0.2 probability that a senior lawyer will be promoted to partner and a 0.15 probability that he or she will leave the firm. There is a 0.03 probability that a partner will leave the firm. The firm never demotes a lawyer. th Let Xn be the status of an employee at the n' year after he or she has been hired, it could be one of the three types of lawyers (junior, senior, or partner) or two types of leaving (either leaving as a partner or leaving as a non-partner). Let state 0-junior, state 1-senior, state 2=partner, state 3= leave as non-partner, state 4= leave as partner The (one-step) transition matrix is P = 0.85 0 0 0 0 0.1 0 0.05 0.65 0.2 0.15 0 0.97 0 0 1 0 0 0 0 0 0 0.03 0 1 (a) Use the fundamental matrix method,…
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