3. A certain reagent is created to test for an infectious disease. The test has an accuracy rate of p = 90%, and the accuracy does not depend on whether or not the patient is actually infected.

a. If four people are tested for the disease, what is the probability that at least three of them receive accurate test results?

b. In an area where q = 5% of people are infected, a man's test result is positive. What is probability that it is a false positive (which means that he is not infected but the test is positive due to inaccuracy)?