One percent of women at age forty who participate in routine screening have breast cancer (prevalence). Eighty percent of women with breast cancer will get positive mammographies (sensitivity). Finally, 9.6% of women without breast cancer will also get positive mammographies (false positives).
(a) In a population of 100,000 women aged forty, how many would be expected to get positive mammographies?
(b) A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?