When I last thought about this, the coronavirus infection rate where I live was about 1 in 2000. This is a very low probability, and even if I did get infected the chances of my getting seriously ill are also fairly low. Unfortunately our intuitions have difficulty with very small probabilities - which means we can easily jump to disastrously wrong conclusions. There are two basic problems.
The first is a very reasonable tendency to assume that very unlikely events just won't happen. There are obvious evolutionary advantages in clarifying one's view of the world by ignoring very unlikely events, so the propensity to think like this may well be hard wired into our minds. So I'm obviously not infected so there's no danger of my passing it on. And if everyone thinks like this ....
The second problem is that our intuitions find it hard to acknowledge that lots of unlikely events can combine to create events that are much more likely. This is hardly surprising if we are wired to ignore events which are very unlikely.
Lets say I have daily meetings in groups of 6. So I meet 5 other people every day. In the first 8 days I'll meet 40 people. The chance that one of them has covid is roughly 40/2000 or 2% - so, from a pessimistic perspective, this is my chance of being infected. But 2% is not too bad. Not worth worrying about!
Now let's imagine everyone's doing the same thing. After the first 8 days, everyone's chance of being infected is now 2%. (To simplify things, we'll assume the original 1 in 2000 infected are either recovered, safely tucked away on a ventilator, or dead) Over the next 8 days everyone will meet another 40 people, so the chance of one of these being infected is about 80% (40 x 2%) - which we'll take to be the chance of my getting infected. (Confession: I've simplified the probability calculations in a way which makes sense with 1/2000 but with 2% is a bit rough - the right answer should be 55%, but this is still more than half.)
So in 16 days we've gone from 1 in 2000 being infected to most people being infected.
If this scenario plays out almost everyone will be infected after a few weeks. Sooner if we meet more people more often, but later if some of the people I meet are from the same household, or if my chances of picking it up from a single infected person are less than 100% - both of which are likely in practice.
