For diagnostic testing, let X = true status (1 = disease, 2 = no disease) and Y = diagnosis (1 = positive, 2 = negative). Let i = P (Y = 1|X = i), i = 1, 2. (a) Explain why sensitivity = 1 and specificity = 1 - 2 . (b) Let denote the probability that a subject has the disease. Given that the diagnosis for mammograms for detecting breast cancer, suppose = 0.01, sensitivity = 0.86, and specificity = 0.88. Given a positive test result, find the probability that the woman truly has breast cancer. Show the calculations.