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Covid infection after vaccination?
Covid vaccines are not perfect, but they're really darn good.
As of 10/18/21, approximately 190M people in the US had been fully vaccinated against Covid-19. The Centers for Disease Control and Prevention (CDC) had received reports of just over 40,000 breakthrough infections who were hospitalized or died (including almost 11,000 deaths).
Of the deaths,
21% had no symptoms or admission was not related to Covid-19
85% were patients older than 65 years of age (hence the booster doses for this group)
This risk of death (less than 1 per 20,000 vaccinated adults) is probably an underestimate. But the majority of the infections and deaths also occurred prior to vaccine booster availability.
The bottom line is that infection after vaccination does occur, the risk of death from infection after vaccination is far lower than without vaccine, and booster doses further decrease this risk.
Not perfect, but pretty good odds.