### Ellipsis

April 24, 2009
– Comments (13)

Assume you conduct breast cancer screening using mammography in a certain region. You know the following information about the women in this region:

* The probability that a woman has breast cancer is 1% (prevalence)

* If a woman has breast cancer, the probability that she tests positive is 90% (sensitivity)

* If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9% (false-positive rate)

A woman tests positive. She wants to know from you whether that means that she has breast cancer for sure, or what the chances are. What is the best answer?

A. The probability that she has breast cancer is about 81%.

B. Out of 10 women with a positive mammogram, about 9

have breast cancer.

C. Out of 10 women with a positive mammogram, about 1 has

breast cancer.

D. The probability that she has breast cancer is about 1%.

answer: see p.55 here

The paper is about "Statistical Illiteracy" ...