A test for a certain disease is found to be 96 accurate mean

A test for a certain disease is found to be 96% accurate, meaning that it will correctly diagnose the disease in 96 out of 100 people who have the ailment. The test is also 96% accurate for a negative result, meaning that it will correctly exclude the disease in 96 out of 100 people who do not have the ailment. For a certain population segment, the incidence of the disease is 6%.

Now suppose the incidence of the disease in another population segment is 30%. Compute the probability that the person actually has the disease, given that his/her test is positive;

Solution

D = the selected person has the disease

Dc = the selected person does not have the disease.

Incidence of disease = 6% i.e P(D) = 0.06   P(Dc) = 0.94

E = Testing result shows positive for the selected person

Ec = Testing result shows negative for the selected person

P(E | D) = 96% and P(Ec | Dc) = 96%

then we calculate the probability that the person actually has the disease, given that his/her test is positive i.e

according to Bayes theorem , we calculate the probability

P(D | E) = ( P(D)*P(E | D))/ P(E)

where P(E) = 0.30

P(D | E) = ( P(D)*P(E | D))/ P(E) = (0.06*0.96)/0.30 = 0.192