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Suppose that one person in 10,000 people has a rare genetic disease. There is an excellent test for the disease; 99.9% of people with the disease test positive and only 0.02% who do not have the disease test positive.

a) What is the probability that someone who tests positive has the genetic disease?

b) What is the probability that someone who tests negative does not have the disease?

My Answers :-

P(D) = 0.00001           

P(D') = 0.99999

P(P/D) = 0.999

P(P'/D) = 0.001

P(P/D') = 0.0002

P(P'/D') = 0.9998

Answer a) $\frac{(0.999)(0.00001)}{(0.999)(0.00001) + (0.0002)(0.99999)}$

Answer b) $\frac{(0.9998)(0.99999)}{(0.9998)(0.99999) + (0.001)(0.00001)}$

Correct me if I am wrong?
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