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 .


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :