Question 17
Points $P$ and $Q$ are chosen uniformly and independently at random on sides $\overline{AB}$ and $\overline{AC}$, respectively, of equilateral triangle $\triangle ABC$. Which of the following intervals contains the probability that the area of $\triangle APQ$ is less than half the area of $\triangle ABC$?
(A) $[\frac{3}{8}, \frac{1}{2}]$ (B) $(\frac{1}{2}, \frac{2}{3}]$ (C) $(\frac{2}{3}, \frac{3}{4}]$ (D) $(\frac{3}{4}, \frac{7}{8}]$ (E) $(\frac{7}{8}, 1]$
(A) $[\frac{3}{8}, \frac{1}{2}]$ (B) $(\frac{1}{2}, \frac{2}{3}]$ (C) $(\frac{2}{3}, \frac{3}{4}]$ (D) $(\frac{3}{4}, \frac{7}{8}]$ (E) $(\frac{7}{8}, 1]$