Mammography and clinical breast examination are the two major techniques used to screen for breast cancer. However, as true for any screening test, they are not completely accurate. If it is determined, based on mammographic ndings, that there is a possibility of breast cancer, this is usually conrmed or disconrmed by a subsequent biopsy. A false positive test is a mammogram positive test that is disconrmed by biopsy. The data in Table 1 were reported in a paper concerning breast cancer screening (Elmore, et al, New England Journal of Medicine 1998; 338(16): 1089-1096). Table 1 False positive breast cancer screening tests over a 10-year period # Screening tests 9762 # False positive tests 631 . Suppose that 5% of all mammograms are obtained from women who truly have breast cancer. What is the proportion of mammograms that will yield test positive results? - Hint: Subdivide the probability of a test positive mammogram into two mutually exclusive components of {test positive mammograms with breast cancer}, and {test positive mammograms without breast cancer}, and use the results of parts (b) and (c) to evaluate each of these components. . What proportion of the test positives will be conrmed breast cancer cases? What is another name for this quantity