2003 AMC 10A Problem 20

A base-$10$ three digit number $n$ is selected at random. Which of the following is closest to the probability that the base-$9$ representation and the base-$11$ representation of $n$ are both three-digit numerals?

$\mathrm{(A) \ } 0.3\qquad \mathrm{(B) \ } 0.4\qquad \mathrm{(C) \ } 0.5\qquad \mathrm{(D) \ } 0.6\qquad \mathrm{(E) \ } 0.7$