1.Sixteen patients need to have their blood tested for a certain disease. Each patient, independently of the others, has a 5% chance of having the disease, and the test is perfectly accurate. Consider two methods of testing them:

Individual method: Test each patient individually.

Pooled method: Combine blood from all 16 patients into one sample and test it. If the combined sample tests negative, then we know that all 16 patients are healthy, so no further tests are needed. If the combined sample tests positive, then someone (we don't know who) has the disease, and in this case we proceed to test all 16 patients individually.

Which method requires fewer tests, on average?

[Hint: For each method, first write down all possible values of "the number of tests that the method requires."]