Jane Street–styleTrader InternQuantitative Trader InternQuestion #488

A bag contains three visually indistinguishable coins: one with a 10% chance, one with a 30% chance, and one with a 60% chance of landing heads. You randomly select a coin and flip it, and it lands heads. What is the probability that if you flip the same coin again, it will land heads? Explain your reasoning.

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State the assumptions, try a simple case, then work toward a general solution. Check the result and explain how it changes if an assumption changes.

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