Composite Sampling for STDs Currently, the rate for sexually transmitted diseases

(STDs) is 213 per 100,000 (based on data from the Centers for Disease Control and Prevention).

When testing for the presence of STDs, the Acton Medical Testing Company saves money by combining blood samples for tests. The combined sample tests positive if at least one person is infected. If the combined sample tests positive, then the individual blood tests are performed. In a test for STDs, blood samples from 10 randomly selected people are combined.

Find the probability that the combined sample tests positive with at least 1 of the 10 people infected. Is it likely that such combined samples test positive?