Question

A certain disease has an incidence rate of 0.2%. If the false negative rate is 8% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.

Answer 1

Answer:

32%

Step-by-step explanation:

Imagine 100000 people are tested.  

Of these 100000:

• 10000080.02= 2000 will have the disease

8% of them:

• 2000*0.08= or 160, will test negative and the remaining
• 1840 will test positive.  

Of the 98000 who do not have the disease, 4% will test positive:

• 98000*0.04= 3920 will test positive

So of the:

• 1840+3920= 5760 total people who test positive,

• 1840 will have the disease

Thus, the probability is:

• 1840/​5760 ​​ ≈0.3194 = 32%

So, out of people who test positive actually 32% has the disease.