Two numbers a and b with 0\le a\le1 and 0\le b\le1 are chosen at random. The number c is defined by c=2a+2b. The numbers a,b and c are each rounded to the nearest integer to give A,B and C, respectively. (For example, if a=0.432 and b=0.5, then c=1.864, and so A=0,B=1, and C=2.) What is the probability that 2A+2B=C?
Answer Choices
A. \frac{15}{32}
B. \frac38
C. \frac12
D. \frac{7}{16}
E. \frac34