25. On the surface of a small pond, there are 11 lotus leaves, marked as $0,1, \cdots, 10$. A frog is on the 1st lotus leaf, and the probability of it jumping to the $N(0<N<10)$-marked lotus leaf is equal to the sum of the probability of it being on the $N-1$-marked lotus leaf multiplied by $\frac{N}{10}$ and the probability of it being on the $N+1$-marked lotus leaf multiplied by $\frac{10-N}{10}$. Assume that each jump of the frog is an independent event. If the frog jumps to the 0-marked lotus leaf, it will be eaten by a snake waiting patiently; if the frog jumps to the 10-marked lotus leaf, it can successfully jump out of the pond. What is the probability that the frog will jump out of the pond without being eaten by the snake? ( ).
(A) $\frac{32}{79}$
(B) $\frac{161}{384}$
(C) $\frac{63}{146}$
(D) $\frac{7}{16}$
(E) $\frac{1}{2}$