Of all 40-year-old women, 1% have breast cancer. If a woman has breast cancer, a mammogram will give a positive indication for cancer 90% of the time. If a woman does not have breast cancer, a mammogram will give a positive indication for cancer 9% of the time. If a 40-year-old woman’s mammogram gives a positive indication for cancer, what is the probability that she has cancer?

Question

Of all 40-year-old women, 1% have breast cancer.  If a woman has breast cancer, a mammogram will give a positive indication for cancer 90% of the time.  If a woman does not have breast cancer, a mammogram will give a positive indication for cancer 9% of the time.  If a 40-year-old woman’s mammogram gives a positive indication for cancer, what is the probability that she has cancer?