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Difficulty: Medium
Category: Market Microstructure
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Topics: probability, random-walk, ruin-probability, mental-math
A confused trader, let's call him Bob, stands at position 1 on a number line. Position 0 represents financial ruin (bankruptcy). At each time step, Bob moves either +1 (representing a winning trade) with probability $p = 2/3$ , or -1 (representing a losing trade) with probability $q = 1/3$ . What is the probability that Bob eventually reaches position 0 and faces ruin?
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