A quality control inspector is examining newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration. Given that a flaw is actually present, let p denote the probability that the flaw is detected during any one fixation.t (a) Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has been detected, the sequence of fixations terminates)? (2-p)p (b) Give an expression for the probability that a flaw will be detected by the end of the nth fixation. 1-(1-p)" (c) If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass inspection? (1− p)³ (d) Suppose 20% of all items contain a flaw [P(randomly chosen item is flawed) = 0.2]. With the assumption of part (c), what is the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also pass if it is flawed)? 0.2(1 p)³ +0.9 X (e) Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed? Calculate for p = 0.4. (Round your answer to four decimal places.) 0.9432 X
A quality control inspector is examining newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration. Given that a flaw is actually present, let p denote the probability that the flaw is detected during any one fixation.t (a) Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has been detected, the sequence of fixations terminates)? (2-p)p (b) Give an expression for the probability that a flaw will be detected by the end of the nth fixation. 1-(1-p)" (c) If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass inspection? (1− p)³ (d) Suppose 20% of all items contain a flaw [P(randomly chosen item is flawed) = 0.2]. With the assumption of part (c), what is the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also pass if it is flawed)? 0.2(1 p)³ +0.9 X (e) Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed? Calculate for p = 0.4. (Round your answer to four decimal places.) 0.9432 X
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![A quality control inspector is examining newly produced items for faults. The inspector searches an item for faults in a series of
independent fixations, each of a fixed duration. Given that a flaw is actually present, let p denote the probability that the flaw is
detected during any one fixation.t
(a) Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has
been detected, the sequence of fixations terminates)?
(2-p)p
(b) Give an expression for the probability that a flaw will be detected by the end of the nth fixation.
1-(1-p)"
(c) If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass
inspection?
(1-p)³
(d) Suppose 20% of all items contain a flaw [P(randomly chosen item is flawed) = 0.2]. With the assumption of part (c), what is
the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also
pass if it is flawed)?
0.2(1 p)³ +0.9
3
X
(e) Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed?
Calculate for p = 0.4. (Round your answer to four decimal places.)
0.9432](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eb54f99-07b7-4922-8aaf-93e58f78f829%2F3f361080-0c8e-4774-a92d-83f930fd10a1%2Fjzo7u5a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A quality control inspector is examining newly produced items for faults. The inspector searches an item for faults in a series of
independent fixations, each of a fixed duration. Given that a flaw is actually present, let p denote the probability that the flaw is
detected during any one fixation.t
(a) Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has
been detected, the sequence of fixations terminates)?
(2-p)p
(b) Give an expression for the probability that a flaw will be detected by the end of the nth fixation.
1-(1-p)"
(c) If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass
inspection?
(1-p)³
(d) Suppose 20% of all items contain a flaw [P(randomly chosen item is flawed) = 0.2]. With the assumption of part (c), what is
the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also
pass if it is flawed)?
0.2(1 p)³ +0.9
3
X
(e) Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed?
Calculate for p = 0.4. (Round your answer to four decimal places.)
0.9432
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