The prevalence of breast cancer in women over 40 in country X is estimated to be 0.8% (i.e., 8 in every 1,000 women in that age group).Mammograms test for the presence of breast cancer. A positive result indicates that the disease is present. A negative result indicates that it is not.The sensitivity of a mammogram test for breast cancer is estimated to be 90%. This is the probability that the mammogram will give a positive result when the person being tested does have breast cancer.The false positive rate for the mammogram is 7.5%. This is the probability that the mammogram will give a positive test result when the person being tested does not have breast cancer.All women who test positive (816) in the mammogram are referred for a further, different examination, which however has the same sensitivity and false positive rates as the first test.What is the probability that a woman referred for this examination and testing positive again, actually does have breast cancer?

Question

radcas87gex5r · Accepted Answer

Ah, the classical cancer detection problem. Let&#039;s use a large sample for this one. Say, 1,000,000 women.Out of these 1,000,000 women:8,000 will have cancer7,200 (90% of 8,000) of them will get a positive test result800 of them will have a negative result (a false negative)992,000 will NOT have cancer74,400 (7.5% of 992,000) of them will get a (false) positive test result917,600 will get a negative resultSo, out of the 81,600 (7,200+74,400) women who get a positive result, only 7,200 of them actually have cancer. Meaning that if your test is positive you have a 9.12% probability to have cancer.Now, if we gather these 81,600 women:From the 7,200 having cancer :6,480 will get a second positive result720 will get a negative oneFrom the 74,400 NOT having cancer :5,580 will get a second (false) positive result68,820 will get a negative oneTo conclude, out of the 12,060 women with a double positive result, 6,480 (53,7%) will actually have cancer. Conversely, out of the 69,540 women having a positive, then negative result, 68,820 (99,0%) actually do NOT have cancer.

The prevalence of breast cancer in women over 40 in country X is estimated to be 0.8% (i.e., 8 in ev

Answered question

Answer & Explanation

New Questions in College Statistics