Extra Problem 4 - Probability Rules Applied - Solution Key

# Extra Problem 4 - Probability Rules Applied - Solution Key...

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EMSE 269 – Elements of Problem Solving and Decision Making Instructor: Dr. J. Rene van Dorp 1 EXTRA PROBLEM 4: SCREENING FOR COLORECTAL CANCER 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. 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 (10%) having colonoscopy actually had cancer. Additional information in the study suggests that, of the patients who were tested, approximately 5 out of 1000 tested negative (no blood in stool) but eventually did develop cancer.

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EMSE 269 – Elements of Problem Solving and Decision Making Instructor: Dr. J. Rene van Dorp 2 A. Create a probability table that shows the relationship between blood in a stool sample and colorectal cancer. Determine P(Cancer|Blood) and P(Cancer| No Blood). Let B = {Blood in Stool}, Let C = {Patient has Colorectal Cancer) “Of the people tested, 10% has blood in their stools”. Therefore: 10 . 0 ) ( = B P “These 10% underwent colonoscopy, and 2.5% of those 10% actually had cancer”. Therefore: 025 . 0 ) | ( = B C P We can thus derive: 0025 . 0 10 . 0 * 025 . 0 ) ( ) | ( ) ( = = = B P B C P C B P
EMSE 269 – Elements of Problem Solving and Decision Making Instructor: Dr. J. Rene van Dorp

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## This note was uploaded on 12/04/2011 for the course BUSINESS 500 taught by Professor John during the Spring '11 term at Kansas.

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Extra Problem 4 - Probability Rules Applied - Solution Key...

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