At the tune-up and brake repair shop, the manager has found that a car willrequire a tune-up with probability 0.8, a brake job with probability 0.35, and neithertune-up, nor brake job with probability 0.1.(A) What is the probability that a car requires exactly one type of repair?(B) What is the probability that a car requires either a tune-up or a brake job?

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Answered: At the tune-up and brake repair shop,…

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 ran a clinical trial of a new drug. 781 volunteers participated in the study. Of these participants, 462 indicated that the drug helped relieve their symptoms. Assume that the efficacy of the drug is the same for any group of people with these symptoms. If we were to administer this drug to a random sample of 6 individuals with symptoms, what is the probability that .. the drug relieves symptoms for all of them? .. the drug fails to relieve symptoms for at least one of them? the drug relieves symptoms for exactly 2 of them? (round to four decimal places)
In a business venture, a man can make a profit of Ksh2,000Ksh2,000 with a probability of 0.40.4 or have a loss of kshs1,000kshs1,000 with a probability of 0.6.0.6. What is his expected profit?
Many fire stations handle emergency calls for medical assistance as well as those requesting firefighting equipment. A particular station says that the probability that an incoming call is for medical assistance is 0.81. This can be expressed as P(call is for medical assistance) = 0.81. Assume each call is independent of other calls. (a) Describe what the Law of Large Numbers says in the context of this probability. (b) What is the probability that none of the next four calls are for medical assistance? (c) You want to estimate the probability that exactly three of the next four calls are for medical assistance. Describe the design of a simulation to estimate this probability. Explain clearly how you will use the partial table of random digits below to carry out your simulation.
Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 60% of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA exam until the first pass. (Assume the trials are independent.) (a) What is the probability that Cathy passes the CPA on the first try? (Use 2 decimal places.)(b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.)
Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 81% of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA exam until the first pass. (Assume the trials are independent.) (a) What is the probability that Cathy passes the CPA on the first try? (Use 2 decimal places.)(b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.)
Peter fails quizzes with probability 1/4, independent of other quizzes. What is the probability that the second and third time Dave fails a quiz will occur when he takes his eight and ninth quizzes respectively?
In a survey, 45% of the interviewees are of age below 30, 30% are between 30 and 50, and 25% are above 50. 90% of the interviewees aged below 30, 60% of the interviewees aged between 30 and 50, and 70% of the interviewees aged above 50 can swim. (a) If a randomly selected interviewee can swim, find the probability that his/her age is between 30 and 50. (b) If a randomly selected interviewee cannot swim, find the probability that his/her age is below 30.
A salesperson goes door-to-door in a residential area to demonstrate the use of a new household appliance to potential customers. At the end of the demonstration, it was found that 1 out of 5 potential customers would place an order for the product. If the salesperson makes 15 demonstrations, what is the probability that between 2 and 5 orders will be made.
A bank is interested in studying the number of people who use the ATM located outside its office late at night. On average, 1.5 customers walk up to the ATM during any 10 minute interval between 8pm and midnight. What is the probability of 3 or more people using this ATM during any 20 minute interval ?
Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 75% of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA exam until the first pass. (Assume the trials are independent.) (a) What is the probability that Cathy passes the CPA on the first try? (Use 2 decimal places.)(b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.)
A car manufacturer produces both sedan and SUV vehicles. The probability that a customer will purchase a sedan vehicle is 0.75. Of those that purchase sedan vehicle, 60% also purchase extended warranty. But only 30% of SUV vehicle buyers purchase extended warranty. A randomly selected buyer purchases extended warranty and a vehicle. What is the probability that the purchased vehicle is sedan?

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