Gerry is now jumping on vertices of a regular hexagon. At each step, he jumps to one of the two neighboring vertices, choosing each possibility with probability $1/2$. Gerry started at vertex $A$.
There is a pool of orange paint at vertex $D$. If Gerry jumps there, he will be stained with orange paint.
What is the probability that he won’t be stained after $25$ jumps?
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