You are a physician who has just examined a woman with a lump in her breast. The textbooks and your experience estimate the probability of a malignant tumor (cancer) in such a lump to be 4/100, that is, 4%. To be safe, you order a mammogram, an X-ray test that classifies correctly (i.e., identifies the tumor type as it really is) 80% of the malignant tumors, and 90% of the benign (harmless) tumors. The test, surprisingly, is positive (that is, the radiologist classified the tumor as malignant). What is the probability that the patient has a malignant tumor now?
my answer was : 0.8*0.04/(0.04*0.8+0.96*0.1) but not sure about if it's 0.1 or 0.2