Anyone have Two Envelopes?

Discrete Mathematics Level 3

Your friend has hit the lottery and, in an act of generosity, decided to give you some money. He chooses a random amount of Rupees \( X \), where \( X \) is a real number between 1,000 and 1,000,000.

He then places Rs. \( X \) in one envelope, Rs \( 2X \) in another and places them both on a table.He then offers you one of them to keep.

You pick one of them up and you find Rs \( 31,416 \) inside.

Now, your friend offers you the opportunity to change your mind and choose the other envelope. But if you change your mind and choose the other envelope, you will have to stick with it.

Given these circumstances, which option has the highest expected value?


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