AMC 12 2016a Problem 23

Three numbers in the interval $\left[0,1\right]$ are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area?

\textbf{(A)}\ \dfrac{1}{6} \textbf{(B)}\ \dfrac{1}{3} \textbf{(C)}\ \dfrac{1}{2} \textbf{(D)}\ \dfrac{2}{3} \textbf{(E)}\ \dfrac{5}{6}