the truth is, a test that is 95% accurate isn’t much use at all. Even the smallest errors can blow up over a large population. Let’s say coronavirus has infected 5% of the population. If you test a million people at random, you ought to find 50,000 positive results and 950,000 negative results. But if the test is 95% sensitive and specific, it test will correctly identify only 47,500 positive results and 902,500 negative results. That leaves 50,000 people who have a false result.

...a whopping 47,500 people who are actually negative—not immune—could incorrectly test positive. Half of the 95,000 people who are told they are immune and free to go about their business might never have been infected yet.

Because we don’t know what the real infection rate is—1%, 3%, 5%, etc.—we don’t know how to truly predict what proportion of the immunity passports would be issued incorrectly.

Chris Murray from the University of Washington’s Institute for Health Metrics and Evaluation told NPR his group’s models predict that come June, “at least 95% of the US will still be susceptible to the virus,” leaving them vulnerable to infection by the time a possible second wave comes around in the winter. Granting immunity passports to less than 5% of the workforce may not be all that worthwhile.

Don't you fuckers make me conjure up 50 more Trumps!