Suppose a disease, Kermyfrogulosis, occurs in 1 out of every 100 people. If you have this disease and it goes untreated, the (only) effect is that your skin turns bright green. Suppose that a test for this disease gives 5% false negatives and 10% false positives.
a) Unfortunately, the treatment for the disease has a 1/5 change of actually causing the symptoms, i.e. turning the skin a bright green color and this effect is independent of whether or not the patient has the disease. This means that if you have the disease, the treatment works 4/5ths of the time to prevent the symptoms and if you don't have the disease the treatment has a 1/5th chance of turning your skin green. Anyone who tests positive is automatically given the treatment. What is the probability that an individual who is tested does not have the disease but is treated and has his skin turn green?
b) The federal government decides to screen the entire population for the disease and then administer the treatment. Will people be more likely or less likely to get bright green skin if such a policy is adopted? Give an estimate of the change in likelihood of getting green skin (example: people will be about 3 times more likely, about 7 times less likely etc.).