Consider a medical practitioner pondering the following dilemma: “If I’m at least 80 percent certain that my patient has this disease, then I always recommend surgery, whereas if I’m not quite as certain, then I recommend additional tests that are expensive and sometimes painful. Now, initially I was only 60 percent certain that Jones had the disease, so I ordered the series A test, which always gives a positive result when the patient has the disease and almost never does when he is healthy. The test result was positive, and I was all set to recommend surgery when Jones informed me, for the first time, that he was diabetic. This information complicates matters because, although it doesn’t change my original 60 percent estimate of his chances of having the disease in question, it does affect the interpretation of the results of the A test. This is so because the A test, while never yielding a positive result when the patient is healthy, does unfortunately yield a positive result 30 percent of the time in the case of diabetic patients who are not suffering from the disease. Now what do I do? More tests or immediate surgery?” 5. Consider a medical practitioner pondering the following dilemma: "If I'm at least 80 percentcertain that my patient has this disease, then I always recommend surgery, whereas if I'mnot quite as certain, then I recommend additional tests that are expensive and sometimespainful. Now, initially I was only 60 percent certain that Jones had the disease, so I orderedthe series A test, which always gives a positive result when the patient has the diseaseand almost never does when he is healthy. The test result was positive, and I was all setto recommend surgery when Jones informed me, for the first time, that he was diabetic.This information complicates matters because, although it doesn't change my original 60percent estimate of his chances of having the disease in question, it does affect theinterpretation of the results of the A test. This is so because the A test, while never yieldinga positive result when the patient is healthy, does unfortunately yield a positive result 30percent of the time in the case of diabetic patients who are not suffering from the disease.Now what do I do? More tests or immediate surgery?"

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Answered: 5. Consider a medical practitioner…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Consider a medical practitioner pondering the following dilemma: “If I’m at least 80 percent certain that my patient has this disease, then I always recommend surgery, whereas if I’m not quite as certain, then I recommend additional tests that are expensive and sometimes painful. Now, initially I was only 60 percent certain that Jones had the disease, so I ordered the series A test, which always gives a positive result when the patient has the disease and almost never does when he is healthy. The test result was positive, and I was all set to recommend surgery when Jones informed me, for the first time, that he was diabetic. This information complicates matters because, although it doesn’t change my original 60 percent estimate of his chances of having the disease in question, it does affect the interpretation of the results of the A test. This is so because the A test, while never yielding a positive result when the patient is healthy, does unfortunately yield a positive result 30 percent of the time in the case of diabetic patients who are not suffering from the disease. Now what do I do? More tests or immediate surgery?”

5. Consider a medical practitioner pondering the following dilemma: "If I'm at least 80 percent
certain that my patient has this disease, then I always recommend surgery, whereas if I'm
not quite as certain, then I recommend additional tests that are expensive and sometimes
painful. Now, initially I was only 60 percent certain that Jones had the disease, so I ordered
the series A test, which always gives a positive result when the patient has the disease
and almost never does when he is healthy. The test result was positive, and I was all set
to recommend surgery when Jones informed me, for the first time, that he was diabetic.
This information complicates matters because, although it doesn't change my original 60
percent estimate of his chances of having the disease in question, it does affect the
interpretation of the results of the A test. This is so because the A test, while never yielding
a positive result when the patient is healthy, does unfortunately yield a positive result 30
percent of the time in the case of diabetic patients who are not suffering from the disease.
Now what do I do? More tests or immediate surgery?"

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