AMC 12 2013a Problem 22

A palindrome is a nonnegative integer number that reads the same forwards and backwards when written in base 10 with no leading zeros. A 6-digit palindrome $n$ is chosen uniformly at random. What is the probability that $\frac{n}{11}$ is also a palindrome?

\textbf{(A)} \ \frac{8}{25} \textbf{(B)} \ \frac{33}{100} \textbf{(C)} \ \frac{7}{20} \textbf{(D)} \ \frac{9}{25} \textbf{(E)} \ \frac{11}{30}