Q. 265.0( 2 Votes )

# A laboratory blood test is 99% effective in detecting a certain disease when its infection is present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

Answer :

Let us assume U_{1}, U_{2}, U_{3} and A be the events as follows:

U_{1} = Person has disease

U_{2} = Person doesn’t has disease

A = Blood test result is positive

From the problem,

⇒

⇒

⇒ P(A|U_{1}) = P(Blood test results shows positive for the person with disease)

⇒

⇒ P(A|U_{2}) = P(Blood test results shows positive for the person without disease)

⇒

Now we find

P(U_{1}|A) = P(The Person has a disease given that the blood test results shows positive)

Using Baye’s theorem:

⇒

⇒

⇒

⇒

⇒

⇒

∴ The required probability is .

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