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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??

gamma
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    Presumably the "percentage protection" is not actually the chance of not getting infected, so your model is missing some details. For that matter, "probability to get Covid" is not well-defined. Probability in the next day? In the next week? Over a lifetime? In the next interaction with another person? When deliberately exposed to an infection? – Misha Lavrov Oct 19 '21 at 15:41
  • My reply here may be of interest. – ryang Feb 08 '22 at 03:42

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