At age 40, 1% of women can be expected to have breast cancer. Of those women with breast cancer, 80% will have positive mammographies. In addition, 9.6% of women who do not have breast cancer will...

At age 40, 1% of women can be expected to have breast cancer. Of those women with breast cancer, 80% will have positive mammographies. In addition, 9.6% of women who do not have breast cancer will have a positive mammography. If a woman in this age group tests positive for breast cancer, what is the probability that she actually has it. Use Bayes’ theorem to solve this problem. (Hint: Letting BC stand for “breast cancer,” we have p(BC) 5 .01, p(1|BC) 5 .80, and p(1| ) 5 .096. You want to solve for p(BC|1).)