Question 16 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? Write the probabilitiy as a decimal rounded to 4 decimal places. Submit Question

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UpStudy AI · Accepted Answer

1. Let $$ p $$ be the probability that a person is vaccinated. We have $$ p = 0.6 $$.

2. Therefore, the probability that a person is not vaccinated is $$ 1 - p = 1 - 0.6 = 0.4 $$.

3. For 3 independent people, the probability that none of them is vaccinated is 
   $$
   (0.4)^3 = 0.064.
   $$

4. Using the complement rule, the probability that at least one of the 3 people is vaccinated is 
   $$
   1 - 0.064 = 0.9360.
   $$

Thus, the probability that at least one person in the group of 3 is vaccinated is $$ 0.9360 $$.
The probability that at least one person is vaccinated is 0.9360.

Question 16
In a large population, 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?
Write the probabilitiy as a decimal rounded to 4 decimal places.
Submit Question

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Question 16 In a large population, 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? Write the probabilitiy as a decimal rounded to 4 decimal places. Submit Question