Solution:

Let represent a person who has a disease, represent a person who does not have a disease, and represent a person who has a positive blood test.

and are events that are complementary to one another.

Then

Then and

Also result is positive given that person has disease)

And (result is positive given that person has no disease)

Given a positive test result, the probability that a person has a disease is .

We have used Bayes’ theorem to arrive at our conclusion.

We acquire the values by substituting them.