Question

The fecal occult blood test, widely used both in physicians’ offices and at home to screen patients for colon and rectal cancer, examines a patient’s stool sample for blood, a condition indicating that cancer may be present. A recent study funded by the National Cancer Institute found that of 15,000 people tested on an annual basis, 10% were found to have blood in their stools. Only these 10% underwent further testing, including colonoscopy, the insertion of an optical-fiber tube through the rectum in order to inspect the colon and rectum visually for direct indications of cancer. Only 2.5% of those having colonoscopy actually had cancer. Additional information in the study suggests that, of the patients who had the fecal occult blood test, approximately 5 out of 1,000 tested negative (no blood in the stool) but eventually did develop cancer.

1. Create a probability table that shows the relationship between blood in a stool sample and colorectal cancer. Calculate P(Cancer|Blood) and P(Cancer|No Blood).

Answer 1

from above data:

		Blood
		Yes	No	Total
Cancer	Yes	0.0025	0.0045	0.007
	No	0.0975	0.8955	0.993
	Total	0.1	0.9	1

P(Cancer |Blood) =0.025

P(Cancer|No Blood) =5/1000 =0.005