There is a virus spreading across the population of a country

There is a virus spreading across the population of a country. There are no obvious symptoms, so it is not possible to determine if someone is a carrier unless they are given a blood test. Medical officials want to study an individual who is carrying the virus, so they plan to randomly select a sample of the population to test. However, there is some argument in determining the size of the sample: if the sample size is too small, there is a risk of not finding any carriers, but if it is too large, resources will be used inefficiently. A decision is made to obtain a sample of 15 individuals. Assuming that 3% of the population is actually infected with the virus, is this sample size adequate? Justify your answer. (3pt)