Q. 335.0( 1 Vote )

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?

Answer :

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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