Suppose that one in 10,000 cargo containers contains a kilogram quantity of plut

Question

Suppose that one in 10,000 cargo containers contains a kilogram quantity of plutonium.
A rst attempt at screening is done by having agents read the manifest, and if the manifest looks to be in order, the container is immediately released. Fifty percent of the containers fall into this category, and the manifest-reading step is 98% accurate at nding the actual material, if it is there. The other fty percent are given a scan. This scan picks up actual weapon-grade material with a 97 percent success rate. Find the BAYESIAN PROBABLITY that if a weapon-usable part gets through, it is from an unscanned container.

Explanation / Answer

P(Passed) = P(Scanned)*P(Passed | Scanned) + P(Unscanned)*P(Passed | unscanned)

= 0.50*0.97 + 0.50*0.98

= 0.975

By Bayes theorem,

P(Scanned | Passed) = P(Scanned)*P(Passed | Scanned) / P(Passed) = 0.50*0.97 / 0.975

= 0.4974

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