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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 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 ...

    Solution Summary

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