Only 1 in 1,000 is afflicted with a rare disease for which a diagnostic test has...
Only 1 in 1,000 is afflicted with a rare disease for which a diagnostic test has been developed. When a person has the disease , the test returns a positive result 99% of the time. However, when a person does not have the disease, the test shows a positive result only 2% of the time. When a person's test results are positive, in order to validate the results, a second test is given. The second test has the same accuracy both for the individuals who have disease and also for those who don't. If a person's first test result is negative, a second test is not necessary. Determine the likelihood that a person has the disease given that the person received two positive test results.
(Hint: Use a probability tree and Bayes' Rule)
Homework Answers
P(result is twice positive)=P(have disease and result is twice positive)+P(not have disease and result is twice positive)=(1/1000)*0.99*0.99+(999/1000)*0.02*0.02=0.00138
hence P(has the disease given result twice positive)
=P(have disease and result is twice positive)/P(result is twice
positive)
=(1/1000)*0.99*0.99/0.00138=0.710217
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