It is breast cancer awareness month. Early detection yields the most favorable treatment outcome. Doctors are divided on when mammograms should start, with some recommending annual mammograms starting at 40 for all women, whereas others recommend biennial mammograms starting at 50 for all women. Current breast cancer statistics indicate that 1 in 8 women will develop "invasive" breast cancer sometime during her lifetime. The sensitivity (correctly identifying breast cancer in a woman that truly has breast cancer) of mammograms is about 78%. According to statistics compiled by the Susan G. Komen foundation, the false positive rate of mammography is about 5.5%.

What is the probability that a woman ultimately does not have breast cancer given that the mammogram indicates that she has breast cancer?

using this Pr[A|B]=Pr[B|A]*Pr[A]

Pr[B]