The f(x,y) in particular is (47+x)/(96+y). Both x and y are real and range from -2 to 2, inclusive. I don't have much of an idea of how to solve this since the problem itself arises from a IRL situation regarding electoral polls. But my mildly respectable freshman knowledge of statiscts tell me some double integral over a probrability mass function might pop up somewhere.
edit: perhaps graphically finding out the portion of the -2<=x<=2 range that satisfies (47+x)/(96+y)>=0.5 works? I'm not really sure if this gives me answer for this problem, but i'm inclined to believe it so.