The Rapid Test is used to determine whether someone has HIV (the virus that causes AIDS). The false-positive and false-negative rates are 0.027 and 0.08, respectively. A physician has just received the Rapid Test report that his patient tested positive. Before receiving the result the physician assigned his patient to the low-risk group (defined on the basis of several variables) with only a 0.5% probability of having HIV. What is the probability that the patient actually has HIV? Please show your working.
(A) 8.76%
(B) 14.62%
(C) 20.15%
(D) 42.96%
(E) 69.11%