In a large population, 52 % 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

This is a binomial distribution with n = 4 and p = .52 .

The Pr(AT LEAST ONE vaccinated) = 1 - Pr( no people vaccinated ).

= 1 - Bin (n=4, k =0, p=.52)

= 1 - C(4,0) × 0.52⁰ × (1-.52)^4-0

= 1 - (1×.48⁴) = .9469158 ≈ .95