> I.e. given 100 choirs there will be a distribution of "not easily infected" individuals with choirs with few off them.
That's a valid point -- one choir alone would not be enough to be the proof, it could still be an accident that such individuals happened to be in one particular choir, but it's not the only such "random sample." Given that we have more "random samples" of different sizes, they can be observed as contributing to the evidence, the logic of the proof is there, and the evidence accumulates, especially as it can be observed that no specific "traits" of the infected could be recognized to bring "the difference" between "less" and "more" easy infections.
One of the arguments supporting the significance in the choir is -- the earlier in the spread of infection we observe such choirs, there's less chance that "100 choirs" from your example were even exposed to the virus, and less chance that that specific choir was exceptional. Similar spreads early in epidemics would also point in non-exceptionality of that one.
That's a valid point -- one choir alone would not be enough to be the proof, it could still be an accident that such individuals happened to be in one particular choir, but it's not the only such "random sample." Given that we have more "random samples" of different sizes, they can be observed as contributing to the evidence, the logic of the proof is there, and the evidence accumulates, especially as it can be observed that no specific "traits" of the infected could be recognized to bring "the difference" between "less" and "more" easy infections.
One of the arguments supporting the significance in the choir is -- the earlier in the spread of infection we observe such choirs, there's less chance that "100 choirs" from your example were even exposed to the virus, and less chance that that specific choir was exceptional. Similar spreads early in epidemics would also point in non-exceptionality of that one.