In a large population, 61 % 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?

In a large population, 61% of the people are vaccinated, meaning there are 39% who are not. The problem asks for the probability that out of the 4 randomly selected people, at least one of them has been vaccinated. Therefore, we need to add all the possibilities that there could be one, two, three or four randomly selected persons who were vaccinated.

For only one person, we use P(1), same reasoning should hold for other subscripts.

P(1) = (61/100)(39/100)(39/100)(39/100) = 0.03618459
P(2) = (61/100)(61/100)(39/100)(39/100) = 0.05659641
P(3) = (61/100)(61/100)(61/100)(39/100) = 0.08852259
P(4) = (61/100)(61/100)(61/100)(61/100) = 0.13845841

Adding these probabilities, we have 0.319761. Therefore the probability of at least one person has been vaccinated out of 4 persons randomly selected is 0.32 or 32%, rounded off to the nearest hundredths.

Ifound this on google “a skewed (non-symmetric) distribution is a distribution in which there is no such mirror-imaging. a "skewed right" distribution is one in which the tail is on the right side. a "skewed left" distribution is one in which the tail is on the left side. the above histogram is for a distribution that is skewed right.” i hope this you for what your looking for