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?
Let events E1, E2, E3 be the following events:
E1 - the event that person has TB and E2 - the event that the person does not have TB
Therefore, Total persons = 1000
Therefore,
Let E be the event that the person is diagnosed to have TB
To find- the probability that the person actually has TB
Using Bayes' theorem to find the probability of occurrence of an event A when event B has already occurred.
is the probability that person actually has TB