Select numbers a and b between 0 and 1 independently and at random, and let c be their sum. Let A, B, and C be the results when a, b, and c, respectively, are rounded to the nearest integer. What is the probability that A+B=C ?
Answer Choices
A. \dfrac{1}{4}
B. \dfrac{1}{3}
C. \dfrac{1}{2}
D. \dfrac{2}{3}
E. \dfrac{3}{4}