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By examining the. chest X-ray, the proba...

By examining the. chest X-ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. In a certain city, 1 in 1000 people suffers from TB. A person is selected at random and is diagnosed to have TB. What is the probability that he actually has TB?

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To solve the problem, we will use Bayes' theorem. We need to find the probability that a person actually has TB given that they have been diagnosed with it. ### Step-by-Step Solution: 1. **Define Events:** - Let \( E_1 \): The event that a person has TB. - Let \( E_2 \): The event that a person does not have TB. - Let \( A \): The event that a person is diagnosed with TB. ...
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