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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

A token moves on three squares 1, 2, 3 in a row. From square 1 or square 3 it always moves to square 2; from square 2 it moves to square 1 or square 3 with probability 1/21/2 each. In the steady state, what is the probability that the token is on square 2? Express your answer as a common fraction.