Breast cancer occurs most frequently among older women. Of all age groups, women in their 60s have the highest rate of breast cancer. The National Cancer Institute (NCI) compiles U.S. epidemiology data for a number of different cancers. The NCI estimates that 3.65% of women in their 60s get breast cancer. Mammograms are X-ray images of the breast used to detect breast cancer. Consider the following data from a case-control study examining a sample of 80 women in their 60s screened for breast cancer:
Screening Test Result | Actual Cancer Status: Breast Cancer | Actual Cancer Status: No Breast Cancer | Total
Mammogram + | 34 | 2 | 36
Mammogram - | 6 | 38 | 44
Total | 40 | 40 | 80
If a woman in her 60s gets a positive mammogram result, what is the probability that she really has breast cancer?
0.94
0.392
0.0328
0.85