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It could be that, but there are also procedural factors as in the one where you have cited.

For example, to my knowledge (at least in Poland) when you are tested for HIV or other infections that can linger undetected they take two samples. That way you need a follow-up only if both of them show different results, since this is how you can usually catch false-positive. There is still a fraction of people with both samples being false-positives, but it is order(s) of magnitude less than with one sample. This actually a great example of Bayesian Process, one of the more important concepts in probability and applied sciences.

I can try and write an example, but I think that it will save both of us some time if I'll just link this:

and here is some extra footage that is also relevant:

I can explain it further if you would have follow-up question after video, so don't take it as me brushing you off ;).