False positive results are not uncommon with mammograms, a test used to screen for breast cancer. For a woman who has a positive mammogram, the probability that she actually has breast cancer is less than 0.05 if she is under 40 years old, and ranges from 0.05 to 0.109 if she is over 40 years old (“Breast Cancer Screenings: Does the Evidence Support the Recommendations?,” Significance [August 2016]: 24–37). If a woman with a positive mammogram is selected at random, are the two events 

B = event that selected woman has breast cancer and

A = event that selected woman is over 40 years old independent events? Justify your answer using the given information.