2016 AMC 12A 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}\qquad\textbf{(B)}\ \dfrac{1}{3}\qquad\textbf{(C)}\ \dfrac{1}{2}\qquad\textbf{(D)}\ \dfrac{2}{3}\qquad\textbf{(E)}\ \dfrac{5}{6}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.