There are lily pads in a row numbered $0$ to $9$, in that order. There are predators on lily pads $4$ and $7$, and a morsel of food on lily pad $8$. 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 $8$ without landing on either pad $4$ or pad $7$?