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The prevalence of a disease D among the population is 3%. There is a diagnostic test...

The prevalence of a disease D among the population is 3%. There is a diagnostic test for disease D. The sensitivity of this test is 99%, this means that the test is positive given that the person has the disease. The specificity of this test is 98%, this means that the test is negative given that the person does not have the disease.

a) Given that a person tests positive, what is the probability that the person does not have the disease?

b) We randomly select 5 people and test them. All of them test negative, what is the probability at least one of them has the disease despite testing negative?

Math   Statistics-And-Probability   
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Answer #1

Let P=event that test is positive, D=event that person has disease. Then accoding to the problem,

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