Interview Question: Exchange Paradox

Sample Question #232 (probability theory – puzzle)
 
[This is a classic probability puzzle known as the Exchange (or Two Envelope) Paradox]
 
It’s year-end bonus time and you and your one-and-only coworker on the Advanced Option Pricing team are shown two sealed envelopes, each containing some amount of bonus money. Your boss tells you that one envelope contains twice as much money as the other envelope. Your boss asks you (not your coworker) to select an envelope, then he asks you if you’d like to switch the envelope. Should you switch?
 
Now, what if you’re allowed to peek into the first envelope you selected? Would you, after peeking, switch the envelope?
 
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