Statistics and silly conclusion, example from August 2021

How come people graduate from schools and still cannot multiply numbers?

Here is what can be found in some news about a country with a huge percentage of vaccinated people: "The majority of people in hospitals who have been diagnosed with covid-19 are vaccinated. This is proof that vaccine does not work!"

And many people write that now. Why stop there? Why not go even further and say that "vaccine kills people!"? It is like saying that because many people with cancer read books we must prohibit reading books. (Just in case, this is a joke, so kids do not use it as an argument with your parents.)

Anyway, let's talk about that statistic. Imagine a country where say 70% are fully-vaccinated. We know that the vaccine is 60%-effective (do not worry that this number is not as big as you expected. It is about just getting Covid. Most of the cases will be so mild, so the infected person won't know about it unless tested), therefore among the vaccinated people approximately 40% have Covid, and these are mostly people with weak immune system. Among them about 10% end up in a hospital. Therefore 0.7 * 0.4 * 0.1 = 0.028 = 2.8% of the whole nation are in the hospital because of covid while being fully vaccinated.

Now let's look at the other 30% of people who are not vaccinated. These are mostly young people who are crazy and go to parties. So let's say 90% of them get covid. But only about 3% of them will actually end up in a hospital as they are young and still strong. Thus you will see 0.3 * 0.9 * 0.03 = 0.0081 = 0.8% of the whole population who are not vaccinated and are in the hospitals because of covid. Certainly 2.8% > 0.8% and this is what we see. But the vaccine is still effective, isn't it?

Oh and by the way, this country and the statistics above are all pretty much real... Can you guess which country is that? :) Also, in this country the number of people in hospital because of Covid was about 700 compared to 4000 last winter.