In Sydney, not one fully vaccinated person is in intensive care. Proves it works, or does it? (Calling all Bayesians)

Of the 44 cases in intensive care in the New South Wales outbreak of COVID-19 not one is fully vaccinated.

Which, say some, proves the power of getting vaccinated. My bias is pro-vaccination, but I'd suggest this is not proof. The sample size is very small and, the 'prior' is that there are very few people vaccinated in Australia (Australia has the lowest rate of vaccination in the OECD, 38 out of 38 ... a piss-poor performance).

If you are unfamiliar with Bayesian probability this is a really good time to check it out. In a nutshell, its important to take into account existing conditions, in this example a low number of people vaccinated suggest that everything else being equal there would be a low number only in ICU. (This is super-simplified).

This is a good starting point (if you need it) for understanding Bayes: