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Question 21

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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?
Give your answer as a decimal to 4 places.
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Answer 1

Answer: 0.9360

Step-by-step explanation: To find the probability that at least one of the three people has been vaccinated, we need to find the probability that none of them have been vaccinated and then subtract that from 1.

The probability that a person has not been vaccinated is 1 - 0.6 = 0.4. Therefore, the probability that all three people have not been vaccinated is:

P(no one vaccinated) = 0.4 × 0.4 × 0.4 = 0.064

So, the probability that at least one of the three people has been vaccinated is:

P(at least one vaccinated) = 1 - P(no one vaccinated) = 1 - 0.064 = 0.936

Therefore, the probability that at least one of the three people has been vaccinated is 0.936 (to 4 decimal places).

Answer: 0.9360