Question

Assume the rate of malignant breast cancer tumors is 1%. That means out of 10,000 mammograms, 100 women will have cancer (10,000 x 0.01 = 100) and the remaining 9900 will have benign tumors or nothing in the mammogram. A study

of 10,000 mammograms finds that they correctly identify a cancerous tumor 85% of the time. A particular
woman gets a positive mammogram. What is her risk of having a cancerous tumor?

Answer 1

When I see this equation, I can properly make the answer come out to 7.8 percent. I do this, by taking the 80 women, and dividing 80 women by the 80 women plus the 950 women, so 80/80+950 (or 80/1030=.078). So I get 7.8%, which should be the right answer.

But when I try to do the same with percentages, it all gets sort of screwy. I take the 80 percent of women (.8) divided by that same 80 percent (.8) plus 9.5 percent of women without cancer who test postive for it (.095). So I get .8/.8+.095=89%.