I've found a really simple explanation of base rate fallacy, which might help some posters:
From Psychology Today:
"Let's suppose you hear that following a party attended by ten people, one vaccinated person and one unvaccinated person became ill from Covid-19. You might think, "Wow, one out of two people (50 percent) who got Covid were vaccinated! So why bother to get vaccinated?"
This is basically the argument you see every day all over social media. But what’s wrong with this way of thinking?
To see the problem, imagine I tell you that at this same party with the two Covid-19 illnesses, both people who became ill were right-handed. Would you then conclude that if you’re left-handed, you’re safe? Probably not. But why not? The answer, of course, is that because there are far more right-handed people in general (90 percent of us are right-handed), there will also be far more right-handed illnesses. In other words, the chances that a person who becomes ill is right-handed is already much higher simply because right-handedness is much more common.
The important point here is the idea that the overall prevalence of something in the population, like right-handedness versus left-handedness, matters when thinking about how likely something is in those two groups. This overall prevalence is the base rate, and our tendency to ignore the overall prevalence is the base rate fallacy. The base rate of being right-handed is very high, so there will be more of just about anything in right- than left-handers, including illness from Covid-19, simply because of this difference in base rate. More right-handers than left-handers eat hamburgers every day. But that doesn’t mean right-handers like hamburgers more than left-handers. It just means there are more right-handers.
Now if we replace “right-handed” with “vaccinated” we can start to see why the base rate fallacy matters in any vaccination discussion. Just like with right-handedness, as vaccination rate increases and there are more vaccinated and fewer unvaccinated people in the population, the absolute numbers of vaccinated people who become ill will increase.
Suppose you now learn that at this party with two Covid-19 illnesses, out of ten people, eight people were vaccinated and two were not. You might still be tempted to say that 1 out of 2 ill people were vaccinated, but that clearly misses the important point about base rates. The right way to think about this is that the one vaccinated person who became ill was one out of eight vaccinated people (12.5 percent), but the one unvaccinated person who became ill was one out of two unvaccinated people (50 percent). Very different, right? The conclusion you’d reach from this example when the base rate is considered is that you would have been about four times more likely to become ill at this party if you’d been unvaccinated. In fact, the real numbers are even more strongly tilted in favor of vaccination. And we're all at this party."