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Hard · Probability & Statistics · Quant Trader interview question · probability, expected-value, paradox, conditional-probability
You are presented with two indistinguishable envelopes, each containing a sum of money. You are told that one envelope contains exactly twice the amount of money as the other. You randomly choose one envelope and open it, finding that it contains 100 dollars. Now, consider the following argument: Let $x$ be the amount in the other envelope. There's a 50% chance the other envelope contains 200 dollars (double your amount). There's a 50% chance the other envelope contains 50 dollars (half