In a population, 2% of the people have a very serious disease. A screening test has been designed to screen for the disease. Of those people that have the disease, 1% will test negative. Of the people that don't have the disease, 5% will test positive. Let D be the event that you have the disease. Let W be the event that you are well (you don't have the disease). Let P be the event that you test positive. Let N be the event that you test negative. With this information, we know the following probabilities: P(D) = 0.02 P(N D) = 0.01 P(P[W) = 0.05 a) What is the probability P(W) that you don't have the disease? b) What is the probability P(W and P) that you do not have the disease and test positive? c) What is the probability P(D and N) that you have the disease and test negative? d) What is the probability P(D and P) that you have the disease and test positive? e) What is the probability P(P) that you test positive? f) What is the probability P(W|P) that you don't have the disease, given that you tested positive