In a large population, 54 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?

Question

Give your answer as a decimal (to at least 3 places) or fraction.

Answer 1

The probability that at least one has been vaccinated = 1 - the probability the NONE have been vaccinated. The probability in the large population that a randomly selected person IS NOT vaccinated = 1 - 0.54 = 0.46.

Since the 3 randomly selected people are independent, the probability that they all are not vaccinated is 0.46^3, so the probability that at least one of them has been vaccinated is 1 - 0.46^3.