Maddenation
Paradoxes
I love paradoxes. I especially love the simple ones that make you laugh because they don’t seem to give you any options to resolve them. They just look at you and point their finger and taunt—“Na, na, na, na, na, na. You can’t figure me out!” This is one of those.
You are set in front of a table with two envelopes on it. You are told that both envelopes contain money, but one (randomly selected) contains twice as much as the other. You select envelope A and open it. It contains $1000, but before you take it out, the person in charge offers you the opportunity to change envelopes. You reason as follows. “Envelope B either contains $500 or $2000. If I give up my $1000, I risk losing $500, but there’s an equal chance of gaining $1000. This sounds like a good deal, so I’ll switch.” Then you realize that if you had initially chosen envelope B, the same argument would apply, causing you to take envelope A instead. This is obviously absurd. What’s going on here?
I again adapted this puzzle from the math forum site. You can take a look, but I did not find their discussion helpful in understanding the paradox.
Dad • Puzzles • 01/08/05 • 6 comments
Comments
Patrick • 01/09/05 • 4:29 PM:Of course, the paradox resolves itself (or at least becomes probabilistically more favorable) if the “person in charge” opens up envelope C and reveals a (very small, folded up) goat, in which case, you know you should switch to envelope B for a 2/3 chance at the bigger prize.
Dad • 01/09/05 • 5:27 PM:Now you’re just being silly.
Dad • 01/10/05 • 6:43 PM:I’m surprised you didn’t say that the plural of paradox should be paradoxen or paradoces.
Patrick • 01/11/05 • 1:18 AM:No, I was going to say that this entry is an appropriate followup to your recent entry “Got any duck food?” “Why do you need duck food?” “Can’t you see I got this paradox to feed!?”
Dan • 01/11/05 • 11:39 PM:Oh my goodness. Hilarious, Pat.
Dad • 01/12/05 • 11:32 AM:Yeah. Who says PC has become a stodgy English professor! He still retains that brilliant sense of humor.
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