what is the probability that at least one then=m has been vaccinate?

Question

in a large population, 52% of the people have been vaccinated. if 5 people are randomly selected, what is the probability that at least one of them has been vaccinate?

Answer 1

x = number of people vaccinated is a binomial variable. The probability that x people will be vaccinated out of n people total when the probability of an individual being vaccinated is p is:

C(n,x) * p^x * (1-p)^(n-x), where C(n,x) = n!/x!(n-x)!

The probability that at least one will be vaccinated = 1 - the probability that 0 will be vaccinated.

or 1 - C(5,0) (0.52)^0 (0.48)^5 = 1 - 0.48^5 = 0.9745