I am currently in a stats class and I'm so terrible with numbers it's not even funny. I have on hw question that seems easy enough and I've worked through it some, but I'm just not sure if it is correct.

Here is the problem:

**The overall prevalence of HIV is 2% of the population. The HIV diagnostic exam has**

sensitivity (probability of detecting HIV given that the person is infected) of 0.98 and specificity

(probability of giving a negative result given that the person is not infected) of 0.95. What is the

probability that the person is infected, given a positive test result? Based on your previous answer,

should HIV testing be required for everyone?

sensitivity (probability of detecting HIV given that the person is infected) of 0.98 and specificity

(probability of giving a negative result given that the person is not infected) of 0.95. What is the

probability that the person is infected, given a positive test result? Based on your previous answer,

should HIV testing be required for everyone?

And here is what I have worked out so far:

P(positive test result / person is infected) = 0.98

or, P(positive test result and person is infected)/P(person is infected) = 0.98

or, P(positive test result and person is infected) = 0.98*0.02 = 0.0196

Can someone please tell me if this is right or if not help me work through it so I can understand!

Thanks!