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Airport scanning Bayesian probability

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1. Suppose an airport scanning device has 98% accuracy in detecting certain kinds of metal objects (98% of people carrying these objects are correctly identified as carriers and 98% of people not carrying them are correctly identified as non-carriers). Suppose that 1% of all travelers actually carry such metal objects. For the 100,000 people who pass through the scanning device each week, do the following:

a. Find the number of people not carrying metal objects who are identified as carriers (false positives).
b. Find the number of non-carriers who are identified as non-carriers (true negatives).
c. Find the number of carriers who are identified as non- carriers (false negatives).
d. Find the number of carriers who are identified as carriers (true positives).
e. What percentage of the people identified as carriers are falsely identified?

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Solution Summary

The solution uses Bayesian probability to determine the probabilities of travelers carrying metal objects based on the accuracy of a security scanner.

Solution Preview

We have two events:

A: The scanning device detects a certain kind of metal object.
B: A person carries this kind of metal object.

From the condition, we have ...

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