Answer :
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 .
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