In a large population, 54 % 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?

In a large population, 54 % 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?
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We will use Q and P to help solve this problem with Q representing the possibility that none of the randomly selected people are vaccinated and P representing the possibility that at least 1 randomly selected person is vaccinated. Because the sum of all probabilities must equal 1, your beginning equation will be P=1-Q. First you need to figure out how much of the population is NOT vaccinated so you would take 100%-54% to get 46%. With that 46%, you can conclude that any given person has the probability of 0.46 of not being vaccinated. To find the value for Q we will take (0.46)^5. Q=(0.46)^5=0.0206. To find P we go back to the original equation of P=1-Q. P=1-0.0206=0.9794. The probability that at least 1 person has been vaccinated is 0.9794.
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