2. A new mammography test kit is devised to screen for breast cancer. The

manufacturer of the kit states that 90% of women who do have breast

cancer test positive for the test. The test also has a 9% false-positive rate

(that is 9% of women without breast cancer test positive.) About 8% of

women who are referred by doctors to take this test (for example, because

they saw unusual lumps in their breast) do have breast cancer.

2

2a) A woman has tested positive. What is the probability that she has

breast cancer?

2b) A nice feature of this test is that applying it to the same patient several

times, then the outcome of each test is independent of previous results.

So if a person who does not have cancer tests positive, the chances

of her testing positive on a subsequent test remains 9%. If a patient

tests positive for the first time and tests positive again for the second

time, what is the probability that she has breast cancer?

2c) A woman has tested negative for breast cancer. What is the proba-

bility that she does not have breast cancer?Statistics and Probability