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What this expected-value interview question tests

This is a medium-difficulty probability question that appears regularly on quant trading and quantitative research interviews. It tests your ability to set up and solve a recurrence relation for expected value, a core skill in pricing, risk, and decision-making under uncertainty.

The problem requires you to identify the states of a system (tracking progress toward a stopping condition) and express the expected cost from each state in terms of the others. Firms value clear state definitions, correct recurrence setup, and the algebraic follow-through — not calculator speed.

• Markov chains and state-based thinking
• Setting up and solving systems of linear equations
• Conditioning on the next event and using the law of total expectation