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What this Markov chain equilibrium question tests

This is an easy puzzle that introduces the concept of steady-state or long-run behaviour in a two-state Markov chain. It's the kind of foundational question quant interviewers use to check whether you can reason about stationary distributions without heavy machinery.

The core skill being tested is your ability to set up and solve a system of balance equations. In the long run, the probability of being in each state stabilises; you find this equilibrium by requiring that the flow into each state equals the flow out. This requires only basic algebra, but the setup—recognising that you need to balance inflows and outflows—is the conceptual crux.

• Markov chain transition matrices
• Stationary distributions and fixed points
• Flow balance and conservation