By examining the chest X-ray, the probabilsity that TB is detected when a person is actually suffering is 0.99. the probability of a healthy person diagonosed to have TB is 0.001. In a certain city, 1 in 1000 persons suffer from TB. A perons is selected at random and is diagonosed to have TB. what is the probability that the actual suffers from TB?

By examining the chest X-ray, the probability that TB is detected when is actually suffering from TB is 0.99 the probability of a healthy person diagonosed to have TB is 0.001. In a certain city, 1 in 1000 persons suffer from TB. A person is selected at random and is diagonsed to have TB. What is the probability that he/she actually sufferes from TB?

In a group of 400 people, 160 are smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the disease. What is the probability that the selected person is smoker and non vegetarian ?

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?

Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected. Of people free of HIV, 99% of the test are judged HIV–ive but 1% are diagnosed as showing HIV+ive. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV+ive. What is the probability that the person actually has HIV?

Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.