There are lily pads in a row numbered $0$ to $10$, in that order. There are predators on lily pads $2$ and $5$, and a morsel of food on lily pad $9$. 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 $9$ without landing on either pad $2$ or pad $5$?