Sampling issue

I want to be able to make comparisons between a specifically selected sample (based on ethnicity) and a randomnly selected sample from the general population. Even though the specific ethnicity represents no more than 10-15% of the population, my randomnly selected sample from the general population contains a much larger proportion of people of this ethnicity. I know this can happen with random samples, and the comparison is going to make differences look small because of the overlap, but how do I articulate the consequences of having a large number of the same people in both samples? What's a better idea? Sample the general population after extracting the specific ethnicity? What are the specific situations in which one approach would be preferred to the other?