It often happens to hear by experts, especially in the field of health, statements about what is possible, understood as “something that has a chance to happen”. I am referring in particular, in the Covid era, to expressions like “Even the vaccinated person can get infected”. This statement is certainly correct. On the other hand if I say “playing the Superenalotto you can win the first prize”, this is also a correct statement, however the probability of winning by playing a single combination is approximately 1/622 million, i.e. almost nothing.
Perhaps in the case of COVID it would be appropriate to add that vaccination does not prevent the virus from affecting a vaccinated person, but that the presence of antibodies should prevent the virus from replicating (remember that viruses are not able to replicate on their own, but must enter the host cell and make it possible for the host cell to reproduce them).So, in the most favorable cases, the vaccinated person shouldn’t even get sick, because the antibodies should block the virus and get rid of it before it can replicate itself. This doesn’t always happen, because it depends on the amount of antibodies present and on the state of the individual’s immune system. In any case, the vaccine certainly prevents, at least in the great majority of cases, the serious disease.
Another statement that is often heard (especially by heavy smokers) is that “even non-smokers can develop lung cancer”. This is also a theoretically correct statement, but that does not take into account the probabilities. It is estimated that the percentage of lung cancers that can be associated with smoking is about 90% for men and 70% for women (data from Aimac, https://www.aimac.it/informazioni-tumori/fattori-rischio-tumori/fumo).
A minimal knowledge of the principles of probability calculation would perhaps be highly recommendable for everyone.
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