Let's address the Israel situation once again.... or you can just go read all the previous posts on the subject.
The proper definition of breakthrough cases is the total number of fully vaccinated cases divided by the number of people fully vaccinated in a population. This is the meaningful number. The number of vaccinated versus unvaccinated in a hospital as a pin-point of time without understanding the larger situation.
It appears you are suffering from
Base Rate Fallacy. This particular article describes it in context of Israel.
Let's provide some insight... as of 3 days ago 78% of the eligible Israeli population has been vaccinated or 60% of the total population is fully vaccinated. For a total of
5.4 million people who are fully vaccinated. Let's assume that 60% of the
50,000 recent active cases in people are among the fully vaccinated. (they are not) -- this would give us a 30,000 (I will note the actual number was 11,563 for age 20 & over in early August). The
Israel Heath dashboard provides detailed information.
So worst case 30,000 breakthrough cases / 5.4 million fully vaccinated is a
0.55% breakthrough case rate (worst case) in Israel.
For a deeper look at Israeli breakthrough cases by age and Simpsons Paradox take a look
here.