The Diamond Detector

In a mine field, there is a $1\%$ chance that a randomly chosen ore contains a valuable diamond. Robols Corp. developed the "DoesThisHaveDiamond" tester, which always detects a diamond when one is present, but gives a false positive (reports a diamond in an ore that has none) $10\%$ of the time. An ore with a diamond is worth $100$ dollars, and an ore without one is worthless. What is the expected value, in dollars, of an ore that tests positive? The answer is in the form $\dfrac{p}{q}$ where $p$ and $q$ are coprime positive integers. Input the answer as the sum $p+q$.