Disease Probability

6

One percent of the population suffers from a certain disease. There is a blood test for this disease, and it is 99% accurate, in other words, the probability that it gives the correct answer is 0.99, regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that she has the disease. What is the probability that she actually has the disease?

(A) 0.99%
(B) 25%
(C) 50%
(D) 75%
(E) 98%

I thought it would just be 0.1*0.99 = 0.0099 but it appears that this is not the case.

From the given you can see that:
probability of having the disease.
probability of not having the disease.
probability of a positive test given the disease.
probability of a positive test given no disease.

The probability of a positive test is:


What the question asks you to find is:
.

Can you finish?