A patient comes to a hospital with symptoms that, in 1% of all cases, indicate a certain rare disease. The test for this rare disease never gives false negatives; if the disease is present, the test result is always positive. However, it gives false positives with a 3% probability even when the disease is not present. Given that the test is positive, find the probability that the patient has the disease. The test comes back positive, so the doctor runs the test again with a different sample. You may assume that false positives occur independently in different samples. Given that the second test also comes back positive, find the probability that the patient has the disease.
A patient comes to a hospital with symptoms that, in 1% of all cases, indicate a certain rare disease. The test for this rare disease never gives false negatives; if the disease is present, the test result is always positive. However, it gives false positives with a 3% probability even when the disease is not present. Given that the test is positive, find the probability that the patient has the disease. The test comes back positive, so the doctor runs the test again with a different sample. You may assume that false positives occur independently in different samples. Given that the second test also comes back positive, find the probability that the patient has the disease.
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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A patient comes to a hospital with symptoms that, in 1% of all cases, indicate a certain rare disease.
The test for this rare disease never gives false negatives; if the disease is present, the test result is
always positive. However, it gives false positives with a 3% probability even when the disease is
not present.
Given that the test is positive, find the probability that the patient has the disease.
The test comes back positive, so the doctor runs the test again with a different sample. You may
assume that false positives occur independently in different samples.
Given that the second test also comes back positive, find the probability that the
patient has the disease.
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