He did it again! What an ingenious strategy. 

You're right, it's mathematically possible, apologies. It is incredibly unlikely (you're still using a number lower than the LOWEST POSSIBLE specificity) but in a situation that ignores all epidemiology it is possible that a modest proportion of positives could be false
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More reasonable: Specificity 99.995% Prevalence 1% 100,000 tests 5 FP 1000 TP FP<.5%
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Using the evidence from Australia: Specificity: 99.9997% Prevalence (in those tested): 0.1% 200,000 tests FP: 1 TP: 200 <1%FP
End of conversation
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