Sensitivity and Specficity (Conditional Probability problem) A medical diagnostic test with sensitivity (true positive rate) of
.95 and specificity (true negative rate) of .90. The disease in question is rare
and occurs in the population with the probability 1/10,000 . A patient is
diagnosed with the disease.
Given the diagnosis, what is the probability that the patient actually has the
disease?

I understand how to determine the True Positive Rate and the True Negative Rate with their specific equations, however i am unsure as to how find the final probability.

Thank you
$p(a|b)=p( a \quad \text{and} \quad b) / p(b)$

$= 0.0001*0.95 / (0.0001*0.95 + 0.9999*0.1)$
Let B be positive diagnosis.

Let A be person is sick. 

$$P(A|B)= \frac{P(A \cap B)}{P(B)} = \frac{0.0001\cdot0.95}{0.0001\cdot0.95+ 0.9999\cdot0.1}\approx 0.000949$$