24When correctly adjusted, a machine that makes widgets operates with a 5% defective rate.However, there is a 10% chance that a disgruntled employee shakes the machine, in whichcase the defective rate jumps up to 30%.(a)Suppose that a widget made by this machine is selected at random and is found tobe defective. What is the probability that the machine had been shaken?

Consider D as an event that machine is defective that is (D=5%) in terms of probability P(D)=0.05…

Answered: When correctly adjusted, a machine that…

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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A certain virus infects one in every 200 people. A test used to detect the virus is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. Which of the following is the probability that a randomly selected person who tests positive is not infected?
The probability of a randomly selected adult in one country being infected with a certain virus is 0.006. In tests for the virus, blood samples from 27 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
Suppose that in the small state of Rhode Island in the USA, the average number of women suffering severe osteoporosis (due to the consumption of dairy products) in any given month is 12. What is the probability that in just one-quarter of a month there will be eight (8) women found suffering severe osteoporosis?
A certain group of women has a 0.29% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
In a certain high school, the probability that a student drops out is 0.1, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25. What is the probability that a randomly selected student gets a GED?
(4) The probability that a person likes coffee is 0.4. If we pick a random sample of 25 people, what is the probability that at least 11 of them like coffee? (5) 61 people booked a seat on a flight, and each person has a 0.9 probability of showing up for the flight. If only 57 seats are available, what is the probability that there will be enough seats for everyone who shows up? (6) You flip a fair coin 8 times. Find the probability that out of the 8 times you flip the coin, you get the exact same number of Heads and Tails.
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.)
The probability of a randomly selected adult in one country being infected with a certain virus is 0.004.In tests for the virus, blood samples from 24 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. The probability that the combined sample will test positive is _____ (Round to three decimal places as needed.)
Suppose there is a 3/10 chance of snow each day this week. What is the probability that it will snow every day this week?
The probability of a randomly selected adult in one country being infected with a certain virus is 0.004. In tests for the virus, blood samples from 15 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
Suppose there is a 11.9% probability that a randomly selected person aged 35 years or older is a jogger. In addition, there is a 15.9% probability that a randomly selected person aged 35 years or older is female, given that he or she jogs. What is the probability that a randomly selected person aged 35 years or older is female and jogs? Would it be unusual to randomly select a person aged 35 years or older who is female and jogs? The probability that a randomly selected person aged 35 years or older is female and jogs is (Round to three decimal places as needed.).
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.)

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