3. (6pts) Suppose that 30 people are to be given a blood test to see who is possibly HIV affected. The obviously laboratory procedure is to examine each person's blood individually, meaning that 30 tests would eventually be run. An alternative strategy is to divide each person's blood sample into two parts: A and B. All of the A's would be mixed together and treated as one sample. If that pooled sample proved to be negative, all 30 people individuals must be clean, and no further testing would be done. If the pooled sample is positive, all 30 B samples would have to be analyzed individually. For a given probability p = 0.5, 0.01 and 0.001 which is the probability that a person is affected with HIV, which type of the tests: traditional one or the pooled one you suggest to use for each value of p? (Hint: define a random variable X to be the number of tests that will be performed if the samples are pooled.)