Question

A medical testing laboratory saves money by combining blood samples for tests, so that only one test is conducted for several people. the combined sample tests positive if at least one person is infected. if the combined sample tests positive, then individual blood tests are performed. in a test for gonorrhea, blood samples from 30 randomly selected people are combined. find the probability that the combined sample tests positive with at least one of the 30 people infected. based on data from the centers for disease control, the probability of a randomly selected person having gonorrhea is 0.00114. round your answer to four decimal places.

Answer 1

The probability is 0.0334.

We will first find the probability that none of the 30 people sampled are infected.  Since the probability of one person being infected is 0.00114, the probability that someone is not infected is 1-0.00114 = 0.99886.  The probability that none of the 30 people are infected would be (0.99886)^30 = 0.966359.  We subtract this from one to find the probability that at least one person is infected:
1 - 0.966359 = 0.0334.