Question

In a large population, 63 % 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? Give your answer as a decimal (to at least 3 places) or fraction.

Answer 1

The probability that at least one of the five people selected has been vaccinated is 0.9934.Finally, the probability that at least one of them has been vaccinated is 1 - 0.0066 = 0.9934.

Step-by-step explanation:

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

The probability that a person has been vaccinated is 63% or 0.63. So, the probability that a person has not been vaccinated is 1 - 0.63 = 0.37.

Assuming the selection of each person is independent, the probability that none of them have been vaccinated is (0.37)^5 = 0.0066.

Finally, the probability that at least one of them has been vaccinated is 1 - 0.0066 = 0.9934.