By examining the chest X-ray, probability that T.B is detected when a person is actually suffering is 0.99. the probability that the doctor diagnoses incorrectly that a person has T.B. on the basis of X-ray is 0.001. in  a certain city 1 in 100 persons suffers from T.B. A person is selected at random is diagnosed to have T.B. What is the chance that he actually has T.B.?

Explanation

To solve the problem, we will use Bayes' theorem, which allows us to find the probability of an event based on prior knowledge of conditions related to the event.

### Given Data:
- Let \( E_1 \): The event that a person is suffering from T.B.
- Let \( E_2 \): The event that a person is not suffering from T.B.
- Let \( A \): The event that the doctor diagnoses the person as having T.B.
- The probability that a person suffers from T.B., \( P(E_1) = \frac{1}{100} = 0.01 \).
- The probability that a person does not suffer from T.B., \( P(E_2) = 1 - P(E_1) = 1 - 0.01 = 0.99 \).
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