What the president says here makes no sense. Biden is claiming that the vaccines are highly effective at preventing serious illness and death (fact check: true ). Yet, he is simultaneously arguing that his mandate is necessary to protect the vaccinated from the hazard of unvaccinated coworkers. If the president’s first claim is true — and it is — then the second one must necessarily be false.

Yes, the vaccinated can still get “breakthrough” infections of COVID-19, but these are exceedingly rare. And even these cases are almost certain not to result in hospitalization or death. According to the Centers for Disease Control and Prevention , “More than 99.99 percent of people fully vaccinated against Covid-19 have not had a breakthrough case resulting in hospitalization or death.” The fully vaccinated are statistically more likely to die from a bee sting than COVID-19 .

Simply put, the vaccinated have next to nothing to fear from COVID-19 — and, therefore, nothing to fear from the unvaccinated.