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At an airport all passengers are checked carefully. Let T with t ∈ {0, 1} be...

At an airport all passengers are checked carefully. Let T with t ∈ {0, 1} be the random variable indicating whether somebody is a terrorist (t = 1) or not (t = 0) and A with a ∈ {0, 1} be the variable indicating arrest. A terrorist shall be arrested with probability P(A = 1|T = 1) = 0.98, and a non-terrorist with probability P(A = 1|T = 0) = 0.001. One in ten thousand passengers is a terrorist: P(T = 1) = 0.0001. What is the probability that an arrested person actually is a terrorist?

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