GATE Civil 2014 Set 2 | GA Question: 10

Question

$10\%$ of the population in a town is $HIV^{+}$. A new diagnostic kit for HIV detection is available, this kit correctly identifies $HIV^{+}$ individuals $95\%$ of the time, and $HIV^{-}$ individuals $89\%$ of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is________