In a large population, 60% 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?

Answer 1

You could examine the probabilities of the following cases:

First person selected has been vaccinated but the other two have not.

Second person selected has been vaccinated but the other two have not.

Third person selected has been vaccinated but the other two have not.

First two people selected have been vaccinated but the last one has not.

Last two people selected have been vaccinated but the first one has not.

First and third people selected have been vaccinated but the second one has not.

All three people have been vaccinated.

Then you could add all these probabilities up, since they are all independent of each other.

There is a simple formula to compute this value, but another approach is even simpler.

The probability is the same as 1 - the probability of all three selected people being unvaccinated.

AND this is 1 - (40%) × (40%) × (40%) = 0.936

(Note that if the probability of being vaccinated is 60%, then the probability of being unvaccinated is 1 - 60%= 40%.)