1. (20 points) For diagnostic testing, let X = true status (1 = disease, 2 = no disease) and Y = diagnosis (1 = positive, 2 = negative). Let m1 = P(Y = 1X = 1) and 72 = P(Y = 1 X = 2). Let y denote the probability that a subject has the disease. (a) Given that the diagnosis is positive, use Bayes' Theorem to show that the probability a subject truly has the disease is P(X = 1Y = 1) = T17 + 72 ( 1 - 7 ) (b) For mammograms for detecting breast cancer, suppose y = 0.01, 71 = 0.86, and 1 - 72 = 0.88. Find the positive predictive value