Question

In a large population, 60 % 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?

Answer 1

Answer:    0.98976

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Explanation:

60% of the people have been vaccinated, so 40% have not.

The probability of getting five people in a row that aren't vaccinated is (0.40)^5 = 0.01024

Subtract this from 1 to get the probability of at least one vaccinated person in the sample of five.

1-0.01024 = 0.98976

This works because the events "at least one vaccinated" and "none vaccinated" are complementary. One or the other must happen, which means the two probabilities add to 1.