Consider any Country where $B_1 = 42.3$% of the people are vaccinated with Pfizer vaccine ($A_1 = 95$% protection against Covid 19 infection), $B_2= 12,4$% got Astra Zeneca ($A_2 = 82$%), $B_3 = 6,9$% Moderna ($A_3 = 95$%) and $B_4 = 3.9$% got the Johnson & johnson vaccine (with $A_4 = 65$%). In that country therefore life $B_5 = 34.5$% unvaccinated people (which have approximately an $A_5 = 10$% protection due to their immune system.
What would be the total probability for a vaccinated person to get Covid?
I would think $p_{tot}(A') = 1 - \sum_{i=1}^{4}p(A_i|B_i)*p(B_i)$ which leads to $50.5$% which is arguably to high. What do I miss here??