A town with a population 10,000 has suffered an outbreak of dragon pox, with 3% of the population being infected. There is a test to diagnose the disease. If you have the dragon pox, the test will correctly register positive 97% of the time and will yield a false negative 3% of the time. If you do not have the dragon pox the test will register that correctly 97% of the time and will yield a false positive 3% of the time. Given that you tested positive for the disease, what is the probability that you actually have dragon pox?
I just do not get this question at all.
Hint
Need Bayes Theorem.
Let $A =$ event that you have the disease.
Let $B =$ event that you tested positive.
Let $(AB) =$ event that both of the events $A$ and $B$ occurred.
Per wikipedia article
$$p(A|B) = \frac{p(AB)}{p(B)}.$$
$p(AB)$ can be calculated as chance of having disease $\times$ chance of getting a true positive.
$p(B)$ can be calculated as the above chance
plus the chance of not having disease $\times$ chance of getting false positive.