If the false negative rate is 8% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.

Question

A certain disease has an incidence rate of 0.5%. If the false negative rate is 8% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.

Answer 1

The probability of having the disease is 0.5%. The probability of a false negative is 8%, so the probability of a true positive is 92%. So the probability of having the disease and a true positive is 0.5% * 92% = 0.46%