Question

A certain disease has an incidence rate of 0.2%. If the false negative rate is 5% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.

Answer 1

P(I)=Incidence rate of a disease= 0.2 %

P(F .N) =False negative rate = 5%

P (F.P)=False positive rate= 2%

Probability that a person who tests positive actually has the disease

=
`(P(F.P)* P(I))/(P(F.P)* P(I)+P(F.N)* P(I))`

=
`(.2*2)/(.2*2+.2*5)`

=
`(.4)/(1.4)`

=
`(2)/(7)`