Question

In a large population, 57% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that at least one of them has been vaccinated? Round your answer to three decimal places.

A) 0.285
B) 0.812
C) 0.995
D) 0.215

Answer 1

To find the probability that at least one of the five randomly selected people has been vaccinated, subtract the probability that none of them have been vaccinated from 1. The probability is approximately 0.954.

Step-by-step explanation:

To find the probability that at least one of the five randomly selected people has been vaccinated, we can find the probability that none of them have been vaccinated and then subtract that from 1.

Since 57% of the people have been vaccinated, the probability that one person has not been vaccinated is 1 - 0.57 = 0.43.

So, the probability that none of the five people have been vaccinated is 0.43^5 = 0.046.

To find the probability that at least one of them has been vaccinated, subtract the probability that none of them have been vaccinated from 1: 1 - 0.046 = 0.954.

Rounding to three decimal places, the probability is approximately 0.954.