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Can you guys help me out on the validity of this claim using Statistics?

So here is the much argued upon chart (2 screenshots of the same chart).

My questions are:

1. Is it valid to compare the percentages of death over the total number of covid-cases for ages <50 between these two groups: unvaccinated and vaccinated (see circled numbers in the table). That is death percentage of unvaccinated is 0.05%, while death percentage of vaccinated is 0.6%.

2. Which brings me to this next point. Based on 1, is it valid to say that the vaccine does not work?

Geez. I can't believe I am posting this on here. But yeah, Statistics is the way to go to save a friend.

Source of data: https://assets.publishing.service.g...le/1014926/Technical_Briefing_22_21_09_02.pdf