Question 16A point $P$ is chosen at random in the interior of equilateral triangle $ABC.$ What is the probability that $\triangle ABP$ has a greater area than each of $\triangle ACP$ and $\triangle BCP?$$\dfrac{1}{6}$$\dfrac{1}{4}$$\dfrac{1}{3}$$\dfrac{1}{2}$$\dfrac{2}{3}$