Compute expected counters after color elimination
Problem
You have a bag with 30 counters: 10 red, 10 yellow, and 10 blue. You draw counters uniformly at random without replacement. Stop the moment the bag contains counters of only two colors (i.e., right after the 10th counter of some color has been drawn and that color is exhausted).
What is the expected number of counters remaining in the bag at that stopping time?
Assumptions/Clarifications
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Draws are without replacement and uniformly random.
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The stopping time is the first time any color is exhausted (its 10th counter is drawn). Ties cannot occur because one counter is drawn at a time.
Constraints & Assumptions
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Preserve the scope, facts, inputs, and requested outputs from the prompt above.
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If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
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Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.
Clarifying Questions to Ask
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Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
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Show enough derivation for the interviewer to follow the reasoning.
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Explain how you would validate the result with simulation or sensitivity checks.
What a Strong Answer Covers
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A correct setup with definitions, formulas, and boundary conditions.
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A step-by-step derivation or estimation plan.
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Interpretation of the result, including uncertainty and practical limitations.
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Checks for assumptions, edge cases, and numerical stability.
Follow-up Questions
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How would the result change if the assumptions were relaxed?
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Can you verify the answer with a simulation?
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What is the most likely source of estimation error?