Consider a screening system that analyzes the luggage that is being loaded to a plane. Each package first goes through a screening device. If it passes the test there, then it is loaded to the plane. If it does not, the package goes to a second screening device. The procedure is similar for the second device: if the luggage passes the test, it is loaded to the plane, if it fails, it is sent to a third device. Packages that passes the test at third device are loladed to the plane, the ones that fail are taken paprt and not loaded to the plane. The screening devices i = 1; 2; 3 are not perfect. For each device, there are two risks: – With probability pi, each device erroneously passes a bag that is dangerous, given that previous devices have correctly rejected the bag. – With probability qi, each device erroneously fails a harmless bag that previous devices have also erroneously failed. Assume that pi; qi > 0 What is the probability that a dangerous package will be loaded to the aircraft? What is the probability that a harmless package will be mistakenly kept off the plane? How does the chance that a hazardous bag is loaded under this three-part screening compare with the chance of its being loaded if any one of the devices was used alone for testing? Why might this three-part screening be preferable to using only one device?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Consider a screening system that analyzes the luggage that is being loaded
to a plane. Each package first goes through a screening device. If it passes the test there, then it is loaded to the plane. If it does not, the package goes to a second screening device. The procedure is similar for the second device: if the luggage passes the test, it is loaded to the plane, if it fails, it is
sent to a third device. Packages that passes the test at third device are loladed to the plane, the ones that fail are taken paprt and not loaded to the plane.
The screening devices i = 1; 2; 3 are not perfect. For each device, there are two risks:
– With probability pi, each device erroneously passes a bag that is dangerous, given that previous devices have correctly rejected the bag.
– With probability qi, each device erroneously fails a harmless bag that previous devices have also erroneously failed.
Assume that pi; qi > 0
What is the probability that a dangerous package will be loaded to the aircraft?
What is the probability that a harmless package will be mistakenly kept off the plane?
How does the chance that a hazardous bag is loaded under this three-part screening compare with the chance of its being loaded if any one of the devices was used alone for testing?
Why might this three-part screening be preferable to using only one device?
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