2005 AMC 12A Problem 14

On a standard die one of the dots is removed at random with each dot equally likely to be chosen. The die is then rolled. What is the probability that the top face has an odd number of dots?

\textbf{(A) } \frac{5}{11} \qquad \textbf{(B) } \frac{10}{21} \qquad \textbf{(C) } \frac{1}{2} \qquad \textbf{(D) } \frac{11}{21} \qquad \textbf{(E) } \frac{6}{11}

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