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User Name Thread Name Subject Posted
BK Lick BS: Monty Hall Problem (212* d) RE: BS: Monty Hall Problem 01 Nov 12


Gnu is very persistent -- I like that in a bloke. Against all odds, I believe I may have devised a thought experiment that might actually convince him to reexamine his so firmly held conviction.

In this scenario:

  • a deck of 52 cards corresponds to the three doors,
  • turning over a card corresponds to opening a door,
  • the Ace of Spades corresponds to the car, and
  • the other 51 card faces correspond to the two goats.
First, Gnu is invited to remove one card at random from a shuffled deck of cards without looking at its face. If his chosen card later turns out to be the Ace of Spades he will win a valuable prize. Otherwise he wins nothing.

Second, Monty examines the deck and turns over 50 of the remaining 51 cards not including the Ace of Spades, leaving one card face down.

At this point, clearly the Ace of Spades is either the card Gnu chose or the one Monty has left face down. Monty now invites Gnu to change his choice from the card he originally chose to the other unknown card.

TWO cards... ONE choice. Will Gnu still insist that either one of these cards has a 50-50 chance of being the Ace of Spades?

Or will he see that the chance of his original card being the Ace of spades is only 1 in 52, while the chance of the other card being the Ace of Spades is 51 in 52?

—BK


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