-1.25 points oi6 test has been designed to detect the presence of a certain dise

Question

-1.25 points oi6 test has been designed to detect the presence of a certain disease. Among people who have the disease, the who do not have the disease, the probability that the test will detect the presence of the disease is 0.04. It is estimated that 5% of the population who take this test actually have the d ase answers to three decimal places.) If the test administered to an individual is positive (the disease is detected), what is the probability that the person actualy has the disease? If the test administered to an individual is negative (the disease is not detected), what is the probability that the person actually does have the disease? not

Explanation / Answer

If the test administered to an individual is positive, probability that person has actually has the disease

= p(detecting disease when it exists) / {p(detecting disease when it exists)+ p(detecting disease when it does not exist)}

= 0.93/ (0.93+0.04)

= 0.959

If the test administered to an individual is negative, probability that person has actually does not have the disease

= p(not detecting disease when it does not exists) / {p(not detecting disease when it does not exist)+ p(not detecting disease when it exists)}

= (1-0.04)/ ((1-0.04)+(1-0.93))

= 0.932

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