Question

[Base Rate Fallacy] Suppose a particular disease has a prevalence of 0.5 % people. A medical test to detect this disease has a false-positive rate of 5 % and diagnoses correctly every person who has the disease. What is the probability that a randomly selected person found to have a positive result actually has the disease? Give your answer to three decimal places.

Answer 1

Ans:

Given that

P(disease)=0.005

P(no disease)=1-0.005=0.995

P(posiitve/disease)=1

P(positive/no disease)=0.05

So,

P(positive)=P(positive/disease)*P(disease)+P(positive/no disease)*P(no disease)

=1*0.005+0.05*0.995

=0.05475

P(disease/positive)=P(positive/disease)*P(disease)/P(positive)

=1*0.005/0.05475

   =0.091