Let S be the square one of whose diagonals has endpoints (0.1,0.7) and (−0.1,−0.7). A point v=(x,y) is chosen uniformly at random over all pairs of real numbers x and y such that 0≤x≤2012 and 0≤y≤2012. Let T(v) be a translated copy of S centered at v. What is the probability that the square region determined by T(v) contains exactly two points with integer coordinates in its interior? <spanclass=′latex−bold′>(A)</span>0.125<spanclass=′latex−bold′>(B)</span>0.14<spanclass=′latex−bold′>(C)</span>0.16<spanclass=′latex−bold′>(D)</span>0.25<spanclass=′latex−bold′>(E)</span>0.32