And note that 20% failure rate assumes that the swab test is not missing any i.e. the immunity test identifies 80% of the patients that the swab identifies. I understand there is a significant false negative rate even with the swabs, though it is hard to know what that is (since we have no way of knowing the virus is there if the swab misses it).
But if the swab is picking up, for argument's sake, 90%, then the immune test is only picking up 80% of 90% i.e. 72% of positives.
And note that 20% failure rate assumes that the swab test is not...
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