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

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 Sally's expected lifespan, in minutes, in this system?

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

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

×