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:Car returned toCar hired fromAirportBeach City1AirportBeachCity1414 1312 34 13Figure 1: Table of car-hire data.403The 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.

The company estimates that the probability of a car being returned to each location is as…

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

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 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…
4. Consider the following table of grades from Mrs. Rossato's English Class. Grades A B D F Totals Males 8 17 12 8 50 Females 12 10 13 10 5 50 Totals 20 15 30 22 13 100 Part A: What is the probability that if a student was female, she got a passing grade? Part B: What is the probability of a male student, given that they failed? Part C: What is the probability of a female student, given that they got a "B"? Part D: What is the probability that the student is a male, given that that they are an "A" student?
section 5.5 A personnel director has two lists of applicants for jobs. List 1 contains names of 24 women and 8 men, whereas List 2 contains the names of 9 women and 16 men. A name is randomly selected from List 1 and added to List 2. A name is then randomly selected from the augmented List 2. Given that the name selected is that of a man, what is the probability that a woman's name was originally selected from List 1? Round your answer to four decimal places, if necessary.
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,…
3. You get a haircut from Barber Shop 1 30% of the time and Barber Shop 2 70% of the time. Barber Shop 1 gives a good haircut 80% of the time and a bad haircut 20% of the time while Barber Shop 2 gives a good haircut 90% of the time and a bad haircut 10% of the time. For any given haircut, the probability that it is a bad haircut from Barber Shop 1 is Barber Shop 2 is and the probability that it is a good haircut from O.06; .63 .2; .73 O.06; .73 .2; .63
. Based on past experience, a company knows that an experienced machine operator will produce a defective item 2% of the time. Operators with some experience produce a defective item 3.5% of the time, and new operators will produce a defective item 9% of the time. At any one time, the company has 53% experienced operators, 33% operators with some experience,and 14% new operators. draw a tree diagram. Given that the item is defective, what is the probability that it was made by a new operator?
5. A commuter must pass through 4 different traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.X P(X) 0 0.05 1 0.25 2 0.35 3 0.20 4 0.15a. What is the probability she is stopped one time on her way to work?b. What is the probability she is stopped at least two times on her way to work

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