In a large population, 63% 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?

Give your answer as a decimal to 4 places.

Respuesta :

Answer:

To find the probability that at least one of the four randomly selected people has been vaccinated, we can calculate the complement of the probability that none of them has been vaccinated.

The probability that a person has not been vaccinated is \(1 - 0.63 = 0.37\).

So, the probability that none of the four people have been vaccinated is \(0.37^4\).

The probability that at least one of them has been vaccinated is \(1 - 0.37^4\).

Calculating:

\[1 - 0.37^4 \approx 1 - 0.0500 \approx 0.9500\]

Rounded to four decimal places, the probability is \(0.9500\).