Let D = 1 denotes the event that an adult male has a particular disease. In the population, it is known that the probability of having this disease is 20 percent, i.e., Pr (D = 1) = 2
Now, suppose that an adult male has a son. Unlike the father's birth, new health policy now requires that all newborn males are tested for the disease. Suppose that a particular adult male's son is tested, and is confirmed not to carry this particular disease. Let S = 0 denote the event that son does not carry the disease.
(a) If the father does, in fact, have the disease, the probability that his son will have the disease is 50 percent.
(b) If the father does not, in fact, have the disease, then the probability that his son will not have the disease is 100 percent.
What is the probability that the father has the disease, given that his son does not have the disease, i.e., Pr (D = 1| S = 0)?