You are the manager of a manufacturing plant and you are responsible for quality control. Each day, a random sample of 10 items is selected from the production line and tested by a quality control technician. A item can be in good condition or defective, and the probability that an item is defective is 0.05. You know by experience that the technician records the result of the test on an item correctly 80% of the time. Let X be the number of items that were recorded as defective by the technician (in the sample of 10 tested items). (a) Find the probability P(X = 1). (b) If the technician recorded one defective item in the sample, what is the conditional probability that there was no defective item in the sample?
You are the manager of a manufacturing plant and you are responsible for quality control. Each day, a random sample of 10 items is selected from the production line and tested by a quality control technician. A item can be in good condition or defective, and the probability that an item is defective is 0.05. You know by experience that the technician records the result of the test on an item correctly 80% of the time. Let X be the number of items that were recorded as defective by the technician (in the sample of 10 tested items). (a) Find the probability P(X = 1). (b) If the technician recorded one defective item in the sample, what is the conditional probability that there was no defective item in the sample?
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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Transcribed Image Text:You are the manager of a manufacturing plant and you are responsible for quality
control. Each day, a random sample of 10 items is selected from the production line
and tested by a quality control technician. A item can be in good condition or defective,
and the probability that an item is defective is 0.05. You know by experience that the
technician records the result of the test on an item correctly 80% of the time.
Let X be the number of items that were recorded as defective by the technician (in
the sample of 10 tested items).
(a) Find the probability P(X= 1).
(b) If the technician recorded one defective item in the sample, what is the conditional
probability that there was no defective item in the sample?
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