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Hard · Probability & Statistics · Quant Trader interview question · probability, random-walk, recurrence
A particularly inebriated individual is standing at the origin (position 0) on a one-dimensional number line. At each discrete time step, they stumble either one unit to the left or one unit to the right, each with a probability of $p = 0.5$. Assume the steps are independent. What is the probability that the drunkard will eventually return to the origin?