Application of Bayes theorem
Screening for disease D.
On average 1 person in 5000 dies because of D. P(D)=0.0002
Let P be the event of a positive test for D.
P(P;D)=0.9, i.e. 90% of the times the screening identifies the disease.
P(P;notD)=0.005 (5 in 1000 persons) false positives.
What is the probability of having the desease if the test says it is positive?
P(D;P)=P(D)P(P;D)/P(P)
P(P)=P(P;D)P(D)+P(P;notD)P(notD)=(0.9)(0.0002)+(0.005)(1-0.0002)=0.005179
P(D;P)=(0.0002)(0.9)/(0.005179)=0.0348
Less than 3.5% of persons diagnosed to have the disease do actually have it.