The "Let's Make a Deal" Paradox

Pete · 05-25-2003, 08:55 AM

OK - This is driving me bananas so I'm challenging you guys to explain this to me so I can convince myself that it's really true.

I was listening to NPR yesterday (weekend edition saturday) and they interviewed some math guy who explained the probability of Let's Make a Deal. The contestant chooses one of three doors, then Monty reveals an empty door and gives the contestant a chance to change their choice. It seems obvious to me that the chances at this point are 50/50. Even chances for switching or not switching. This guy says that's not the case. The chance of getting the right door if you switch is double that if you don't switch (2/3 to 1/3). But he didn't go on to explain any further. ARRRGH

So this morning I woke up Griff cause it was driving me crazy. Then I went online to look it up and found this link. I think I understand the way thry're explaining it but my intuition is still fighting me.

Basically, your chances of guessing the wrong one are 2/3. If you guess the wrong one, Monty must pick the other wrong one so by switching, you get the right one. I guess it all boils down to the fact that you decrease Monty's choices by picking the wrong one. How could you explain this to someone without p-ing them o?

05-25-2003, 08:55 AM	#1
Pete Resident President Join Date: Apr 2003 Posts: 81	The "Let's Make a Deal" Paradox OK - This is driving me bananas so I'm challenging you guys to explain this to me so I can convince myself that it's really true. I was listening to NPR yesterday (weekend edition saturday) and they interviewed some math guy who explained the probability of Let's Make a Deal. The contestant chooses one of three doors, then Monty reveals an empty door and gives the contestant a chance to change their choice. It seems obvious to me that the chances at this point are 50/50. Even chances for switching or not switching. This guy says that's not the case. The chance of getting the right door if you switch is double that if you don't switch (2/3 to 1/3). But he didn't go on to explain any further. ARRRGH So this morning I woke up Griff cause it was driving me crazy. Then I went online to look it up and found this link. I think I understand the way thry're explaining it but my intuition is still fighting me. Basically, your chances of guessing the wrong one are 2/3. If you guess the wrong one, Monty must pick the other wrong one so by switching, you get the right one. I guess it all boils down to the fact that you decrease Monty's choices by picking the wrong one. How could you explain this to someone without p-ing them o?

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