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 suffer from TB. A person selected at random and is diagnosed to have TB. What is the probability that be action has TB?

Question

$\begin{array}{1 1} \large\frac{110}{221} \\\large\frac{20}{221} \\ \large\frac{15}{221} \\ 0 \end{array} $