Question
Gotham City has 1 million citizens. There are 100 terrorists and 999,900 non-terrorists. Recently, the city installed surveillance cameras to all of the subway entrances.
Gotham City has 1 million citizens. There are 100 terrorists and 999,900 non-terrorists. Recently, the city installed surveillance cameras to all of the subway entrances. These cameras are connected to a newly invented facial recognition system; it can identify terrorists with very high accuracy. If the camera scans a terrorist, the system will report "Terrorist" 100% of the time. If the camera scans a non-terrorist, the system will report "Non-Terrorist" 99% of the time, and report "Terrorist" 1% of the time.
Suppose now that the system reported "Terrorist" on a citizen of the city. What is the chance that the citizen is a terrorist?
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