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# A test for detection of a particular disease is not fool proof. The test will correctly detect the disease 90% of the time, but will incorrectly detect the disease 1% of the time. For a large population of which an estimated 0.2% have the disease, a person is selected at random, given the test, and told that he has the disease. What are the chances that the person actually have the disease?

Let us assume U1, U2 and A be the events as follows:

U1 = Person actually has a disease

U2 = Person doesn’t has a disease

A = detection of disease

From the problem  P(A|U1) = P(Test correctly detected) P(A|U2) = P(Test incorrectly detected) Now we find

P(U1|A) = P(The person actually has the disease and correctly detected)

Using Baye’s theorem:     The required probability is .

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