75 million foreigners are expected to visit the United States in 2017. Let us su

Question

75 million foreigners are expected to visit the United States in 2017. Let us suppose that 1,000 have criminal intentions. The Department of Homeland Security is tasked with stopping these people at the border. To save the cost of hiring human agents at the border, DHS is evaluating the latest gizmo invented by our AI entrepreneurs Ben and Lem. Their gizmo, fueled by the latest machine-learning hype, can automatically detect people with criminal intent with 99.9% accuracy. If a person does have criminal intent the gizmo will raise an alert with probability 0.999. If a person is innocent, then with probability 0.999 the gizmo will not raise an alert. In other words, the probability that they make a mistake either way is only 0.001.

a) If the gizmo issues an alert for a person, what is the probability that person has criminal intent?

b) Ben and Lem hire machine learning experts to improve the accuracy of their gizmo to 99.999%. What is the probability that an alert is raised for an innocent person?

Explanation / Answer

(a)

Probability = 999/75998 = 0.0131

(b)

Probability = 744.99/74999000 = 0.000009933

Alert No alert Total Criminal 0.999 * 1000 = 999 1000 - 999 = 1 1000 No criminal 74999000-74924001 = 74999 0.999 * 74999000 = 74924001 75000000 - 1000 = 74999000 Total 75998 74924002 75000000

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