(solution) According to the National Cancer Institute, for women between 50 and 59, there is a 2.38% chance…

(solution) According to the National Cancer Institute, for women between 50 and 59, there is a 2.38% chance…

According to the National Cancer Institute, for women between 50 and 59, there is a 2.38% chance of being diagnosed with breast cancer. Screening mammography has a sensitivity of about 85% for women over 50 and a specificity of about 95%. That is, the false-negative rate is 15% and the false positive rate is 5%. If a woman over 50 has a mammogram and it comes back positive for breast cancer, what is the probability that she has the disease?