AMC 8 2011 Problem 12

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other? $\textbf{(A) } \frac14 \textbf{(B) } \frac13 \textbf{(C) } \frac12 \textbf{(D) } \frac23 \textbf{(E) } \frac34$