AMC 12 2019b Problem 16

There are lily pads in a row numbered $0$ to $11$, in that order. There are predators on lily pads $3$ and $6$, and a morsel of food on lily pad $10$. Fiona the frog starts on pad $0$, and from any given lily pad, has a $\frac{1}{2}$ chance to hop to the next pad, and an equal chance to jump $2$ pads. What is the probability that Fiona reaches pad $10$ without landing on either pad $3$ or pad $6$?

$\textbf{(A) } \frac{15}{256} \textbf{(B) } \frac{1}{16} \textbf{(C) } \frac{15}{128} \textbf{(D) } \frac{1}{8} \textbf{(E) } \frac14$