1. The answer that you found in 5.36 is probably much lower than the answer that you expected, knowing that 80% of women with breast cancer have positive mammographies. Why is it so low?
2. What would happen to the answer to Exercise 5.36 if we were able to refine our test so that only 5% of women without breast cancer test positive? (In others words, we reduce the rate of false positives.)
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).)
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