About this question
Medium · Market Microstructure · Quant Trader interview question · 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?