Use Bayes' rule to find the indicated probability. The incidence of a certain disease on the island of Tukow is 4%. A new test has been developed to diagnose the disease. Using this test, 91% of those who have the disease test positive while 4% of those who do not have the disease test positive (false positive). If a person tests positive, what is the probability that he or she actually has the disease?

Question

Mathematics

Giovanni Hansen

31 January, 06:28

Use Bayes' rule to find the indicated probability. The incidence of a certain disease on the island of Tukow is 4%. A new test has been developed to diagnose the disease. Using this test, 91% of those who have the disease test positive while 4% of those who do not have the disease test positive (false positive). If a person tests positive, what is the probability that he or she actually has the disease?

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Answers (2)

Know the Answer?

Tasha · Answer 1

I think the answer is 0.487

Kamora Esparza · Answer 2

These are the events in the question above:

D - has disease

H - healthy (does not have disease)

P - tests positive

It is the probability that a person has the disease AND tests positive divided by the probability that the person tests positive.

Sick, + [.04*.91] =.0364

Sick, - [.04*.09] =.0036

Healthy, + [.96*.04] = 0.0384

Healthy, - [.96*.96] =.9216

.0364 / (.0364 +.0.0384) = 0.487