Base Rate Fallacy vs. Population of Germany

There are 80 Million people living in Germany. The article in http://www.spiegel.de/politik/deutschland/islamisten-in-deutschland-wie-bedroht-ist-die-innere-sicherheit-a-1011912.html claims that 230 of them are in a file for radical islamists. Let's assume they are all actual evil people instead of suspects that may or may not be actually dangerous.

That's 230 out of 80,000,000 people, or a base rate of 0.00028%.

Let us assume we can check for terrorists with a special scanner. In a pro mille of all cases, 0.1%, the scanner will flag a good citizen erroneously as a terrorist. This leaves us with 80,000 upstanding citizens as false suspects.

In a pro mille of all cases, 0.1%, the scanner will also flag an actual terrorist as a law abiding citizen. This leaves us with zero undetected terrorists. That is, the scanner will actually catch all real terrorists, and in total we will have 80224 suspects.

That is, 224*100/80224 = 0.27% of our suspects will be actual terrorists, and 99.72% of our suspects will be actual law abiding citizens.

Let's improve the test 100 times, so the error rate is one pro mille of a percent, or one in 100,000.

Now we have 1024 suspects, out of which 224 (22%) will be terrorists, and 800 people, 78%, will be actual good citizens - 4 in 5 suspects will still be innocent.

TL;DR: If you are scanning for something rare you are fucked. You will have all of the targets in your suspect list and still are none the wiser until after the explosions, even if you have tools of impossible precision.
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Base Rate Fallacy
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