Hi Julien,
This will be more relevant later in the email, but I want it at the top. Your probability calculations are just wrong, and I can show it with a simple example: Imagine you flip a coin 3 times in a row, and you want to know the probability that at least one flip will be heads. The probability of getting heads for any individual flip is 50%, so by your logic the probability of getting heads at least once in those 3 flips should be 1x0.5 + 1x0.5 + 1x0.5 = 1.5 or 150%. Obviously you can't have a probability higher than 100%, but you can also see for yourself that it's possible to get 3 tails in a row.
(I am not a huge expert on either propabilities or infections diseases)
The problem with simplified models is that they are simply not representing reality and for that reason their conclusions are not generalisable.
The key point is that getting sick is *not* a binary, independent event. People get sick by *accumulating* exposure to the viral agent in sufficient quantity over sufficiently short time so that their particular immune system fails to overcome the incoming viral load. That means that after you have been to one workshop (with 50% chance of being infected there) and you enter the second workshop (which would also have a 50% of you getting infected there), even if you are *not* infected yet, you are entering the room with a significant viral load already in your system. The probability of getting sick is no longer 50% for you now, it is *much* higher. Maybe not 100% yet, but it could be close to that. And if you follow that up with a third workshop ... your chances of getting sick then are for sure over 100%. Does over 100% have a meaning? Yes. That means that even if you cut the third workshop short, you are still certain to get sick. You are still at 100% even after reducing the risk.
Don't think of it as flipping coins.
Think of it like radiation exposure. You can't use statistical tools to add up multiple exposure events to determine death chances. You have to add up the exposure and then calculate the death chance from total exposure. If you do it any other way, you will get wrong answers.
Then you can also consider that "probability of getting sick" is also not really a probability as such. It is actually an _expression_ of how many people on average just have lower exposure thresholds inherently. So with longer low level exposures what you get is that (instead of 100 people flipping coins each time a new workshop is started) you actually get *all* people with low thresholds getting sick with 100% certainty quite quickly while people with high thresholds never get sick at all. We see this in probability scope only because we do not know the thresholds of individual people in advance.
So in summary - a simplified infection model will only give a good answer in the *exact* case it was simplified for (single event, single exposure), but if you try to make any operations on it (like adding multiple events) you will get answers that do not match the underlying reality.
What does this mean for event policy? Again, I am no expert. But my humble opinion is that, with sufficient numbers of people, events and infections, it becomes certain that people with low infection threshold will get infected. Even with the most drastic self-isolation measures for *detected* infections. The only two measures that can help avoid infections are: people with low thresholds not attending the event(s) or low threshold people using any available tools to increase their personal infection thresholds (vaccination, health boosters, good sleep, lots of water, ...). I understand that this might not look like an empathic opinion and thus might not be popular. However, I do believe this is the position that is most consistent with our current understanding of how infections work in large groups.
-- Best regards,
Aigars Mahinovs