Just One Jump!

Discrete Mathematics Level 2

An infinite line of stepping stones stretches out into an infinitely large lake.

A frog starts on the second stone.

Every second he takes a jump to a neighboring stone. He has a 50% chance of jumping one stone closer to the shore and a 50% chance of jumping one stone further away from the shore.

What is the expected value for the number of jumps he will take before reaching the first stone (the one closest to the shore)?

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