Maxdama there are closed envelopes with $2, $4, $8, $16, $32, and $64 lined up in sorted order in front of you. two envelopes next to each other are picked up and shuffled. one is given to you and one is given to your friend. you and you friend then open your own envelopes, look inside, and then decide whether or not to offer to trade. if you both agree to trade, then you will swap. assume you open your envelope and see $16. should you offer to trade?

No, I wouldn't trade.

Explanation:

Originally there were 6 envelopes with money, so both my friend and I had equal chances (1/6) of getting X amount of money.

Since I got $16, that means that out of the remaining 5 possibilities, only 2 of them contain an amount higher than $16. And one of those possibilities is $64 which is the highest possible amount. If my friend has $64 in his envelope, he will definitely not trade, so that eliminates the $64 possibility.

The only four possibilities left are $2, $4, $8, and $32. Only one of them is higher than $16, while three are lower. So the chance that I get less than $16 is 3/4 or 75%.

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