Suppose that you have a large population you wish to test for a certain characteristic in their blood or urine (for example, testing all NCAA athletes for steroid use or all US military personnel for a particular disease). Each test will be either positive or negative.
In this problem, we are assuming that there are no false positive or false negative tests. Since the number of individuals to be tested is quite large, we can expect that the cost of testing will also be large. How can we reduce the number of tests needed and thereby reduce the costs?