# Jumpy, Patient Frog Named Sally And A Math Problem About Her Life-III

A frog, namely, Sally, is jumping about the vertices of a hexagon, $$ABCDEF$$ , each time jumping to one of the adjacent vertices with equal probability. Let Sally start her daily workout in $$A$$, and a mine be located in $$D$$. Every second Sally must make her random jump (as described above). What is the probability that Sally will be alive after $$3133$$ seconds, expressed as a decimal (and probably in scientific notation)?

As a bonus, can you generalise for $$n$$ seconds?

This problem is a part of my froggy, soggy set.

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