By examinin

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

U₁ = Person having T.B

U₂ = Person not having T.B

A = Diagnosing T.B disease

From the problem:

⇒

⇒

⇒ P(A|U₁) = P(diagnosing T.B disease for the person who actually having T.B)

⇒ P(A|U₂) = P(diagnosing T.B disease for the person who don’t actually have T.B)

⇒

Now we find

P(U₁|A) = P(The person has T.B and diagnosed T.B)

Using Baye’s theorem:

⇒

⇒

⇒

⇒

⇒

∴ The required probability is .