Linear AlgebraChallengeMarkov Chains & Long-Run Behavior
Markov Chains & Long-Run Behavior · Challenge problem
Three cards lie in a row in their original order. Each step, with probability nothing happens, and otherwise one of the three pairs of positions is chosen (each with probability ) and those two cards are swapped. What is the probability that after exactly steps the cards are back in their original order? Express your answer as a common fraction.