Question

7. A genetic disorder occurs with probability 1/2000 . There is a test for this genetic disorder. If you have the disorder, then you test positive 90% of the time. If you don’t have the disorder, then you test negative 90% of the time.

If you test positive, what is the probability that you have the disorder?

Answer 1

Solution:

Given:

P( a genetic disorder) = 1/2000

Let GD = Genetic Disorder and NGD = No Genetic Disorder

thus we have:

P( GD) =1/2000 and

P( NGD) = 1 - P(GD) = 1 - 1/2000 = 1999/2000

There is a test for this genetic disorder. If you have the disorder, then you test positive 90% of the time.

Let TP = Test Positive and TN= Test Negative

thus

P( TP | GD) = 0.90

thus

P(TN | GD) = 0.10

and

P(TN | NGD) = 0.90

then

P(TP | NGD) = 0.10

We have to find:

P( GD | TP) =............?

Using Bayes rule:

Thus  the probability that you have the disorder given test positive =