In a large population, 51% of the people have been vaccinated. If 4 people are randomly selected, what is the probability that at least one of them has been vaccinated?

Answer 1

The easiest way to solve this problem is to determine the probability that none of the four randomly selected people have been vaccinated and use that to determine the answer.

Since the population is large, we can assume each of the four people independently has a 51% (.51) chance of being vaccinated, which means that each of them has a .49 chance of being unvaccinated. The probability that all four of them are unvaccinated is (.49)4 ≈ .0576. Thus the probability that at least one of them has been vaccinated is approximately 1 - .0576 = .9424 or about 94%.