A point P is chosen at random in the interior of equilateral triangle A B C. What is the probability that \triangle A B P has a greater area than each of \triangle A C P and \triangle B C P ?
Answer Choices
A. \dfrac{1}{6}
B. \dfrac{1}{4}
C. \dfrac{1}{3}
D. \dfrac{1}{2}
E. \dfrac{2}{3}