Question

in a large population, 68% 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? give your answer as a decimal to 4 places.

Explanation:

Step1: Find the probability of not vaccinated

The probability of a person not being vaccinated is \(1 - 0.68 = 0.32\).

Step2: Probability none are vaccinated

For 5 people, the probability that none are vaccinated is \(0.32^5\) (since each selection is independent). Calculate \(0.32^5 = 0.32\times0.32\times0.32\times0.32\times0.32 = 0.0033554432\).

Step3: Probability at least one vaccinated

The probability of at least one vaccinated is \(1 - \) probability none are vaccinated. So \(1 - 0.0033554432 = 0.9966445568\). Rounding to 4 decimal places gives \(0.9966\).

Answer:

\(0.9966\)