Checking All the Boxes

I'm not 100% sure this is an accurate statement, but here's a thought. When we order labs, it's easy to check all the boxes: CBC, chem-7, electrolytes, LFTs, pregnancy test, etc. But here's the problem: if you take a normal person and order 1 test, you have a 5% false positive rate (if the tests are calibrated to p=0.05). If you order 5 tests, you have a 23% likelihood of one false positive. 20 tests, and you're up to 64% likelihood of a false positive. If you order 100 tests on a normal person, you're almost guaranteed to have at least one false positive (99.4%). This is based on tests having 95% sensitivity which isn't horrible (though I admit many tests have better sensitivities than that). This is the reason why I think data mining microarrays is a statistically ridiculous idea.