Triangle A B C is a right triangle with \angle A C B as its right angle, m \angle A B C=60^{\circ}, and A B=10. Let P be randomly chosen inside \triangle A B C, and extend \overline{B P} to meet \overline{A C} at D. What is the probability that B D>5 \sqrt{2} ?
Answer Choices
A. \dfrac{2-\sqrt{2}}{2}
B. \dfrac{1}{3}
C. \dfrac{3-\sqrt{3}}{3}
D. \dfrac{1}{2}
E. \dfrac{5-\sqrt{5}}{5}