2025 AMC 12A Problem 22

Three real numbers are chosen independently and uniformly at random between 0 and 1. What is the probability that the greatest of these three numbers is greater than 2 times each of the other two numbers? (In other words, if the chosen numbers are a \ge b \ge c, then a \gt 2b.)

\textbf{(A)} \dfrac{1}{12} \qquad \textbf{(B)} \dfrac{1}{9} \qquad \textbf{(C)} \dfrac{1}{8} \qquad \textbf{(D)} \dfrac{1}{6} \qquad \textbf{(E)} \dfrac{1}{4}

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