Question

A diagnostic test for a certain disease is believed to be 90% accurate in detecting the disease when in fact the person has the disease. Also, the test is believed to be 90% accurate in denying the disease when in fact the person does not have it. Only 1% of the population has the disease. A person is selected at random and the diagnostic test confirms the presence of the disease, what is the probability that the person actually has the disease?

Answer 1

Answer)

Lets say we have a sample size of 1000

It is mentioned that only 1% have the disease

So, 1% of 1000 = 10 have the disease and 990 do not

So, among those 10, 9 will be detected with the disease (as it is mentioned that 90% of the time person will be detected with the disease if he has the disease)

So,, true positive = 9

False negative = 10 - 9 = 1

Now if the person do not have the disease

Then he would not detected with the disease 90% of the time

True negative = 90% of 990 = 891

False positive = 990 - 891 = 99

Probability is given by favorable/total

Total = positive (presence of disease) = true positive + false positive = 9 + 99 = 108

Favorable = actually has the disease = true positive = 9

Required probability is 9/108 = 0.0833