Conditional probabilities and HIV tests - Healthcare Assignment

Healthcare Assignment:

In order to calculate the how well HIV tests work, the following samples were taken from known HIV+ patients and HIV- patients: Test result         Known HIV+           Known HIV free Positive             990                             15 Negative           10                               985 Questions: a) What is the sensitivity of the HIV test? b) What is the specificity of the HIV test? c) A patient goes to a clinic and gets an HIV test. She is dismayed to learn that it comes back positive. Now we are going to calculate the probability that she actually is carrying the virus. Put another way, we want to know: P(HIV+ | T+)