Just Don't Drink In 3-Dimensional Space

A drunkard walks out of a bar at midnight. He is in 3-dimensional space of an infinite size. The probability of his stepping 1 step forward, backward, left, right, up or down is equal. Calculate the probability (to two decimal places) of his (eventually) returning to the bar.

Details and Assumptions:

  • Assume the bar is a point particle at the origin.

  • We require the probability that he will, at any point in time, return to the bar.

  • Do not try this at home.


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