02-18-2006, 08:39 PM
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AdultTubeSubmits.com
Industry Role:
Join Date: Dec 2003
Location: The Netherlands
Posts: 10,598
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Quote:
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Originally Posted by Sagi_AFF
It's actually not a different game. You are getting both doors by switching only one is opened now.
FACT: If you didn't pick the right door then when you switch it will always be behind the door you switch to.
What are the odds that you picked the right door?
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I looked it up at wikipedia and I think I get it now on the hand of this example:
Card game experiment
Consider the problem as a card game where the goal is to end up with the ace of spades. Doing this may make the answer easier to understand and provides a way anyone can run a simple experiment. Take three cards including the ace of spades. Shuffle them and deal one to the "player" while you (the "host") keep two. Looking at the two, discard one so long as it is not the ace of spades. Should the player switch? To amplify the effect, do this again using the entire deck. Deal one card to the player while you keep 51 and (looking at the 51) discard 50 so long as none of them is the ace of spades. By switching, the player will nearly always win (51 out of 52 times).
For a more thorough walkthrough of this experiment, consider two players. Player A and Player B take the 13 diamond cards out of a standard deck of cards. The cards are shuffled, and then Player A receives one card face-down and is not permitted to see the card's face. Player B receives the other 12 cards, and he may look at them. Both players are trying to wind up with the ace of diamonds in their hand.
Question: Player A received one card. Player B received twelve cards. What are the chances that the ace is currently in Player B's hand? Answer: Twelve out of thirteen.
Player B has twelve cards and can examine the card faces. At least eleven of them are not the ace. Player B takes out eleven non-ace cards from his hand and lays them down face-up.
Question: Player B did not discard the ace (which he may not even have). No cards have moved from one hand to the other. Therefore, if the ace was in Player B's hand at the beginning, it is still there now. What are the chances that the ace is currently in Player B's hand? Answer: Since the chances depend only on whether or not he originally received the ace, the chances are still twelve out of thirteen.
Player A now has an option: he can stay with the one card he was originally dealt (which he hasn't looked at), or he can switch his hand with Player B's hand, which was originally dealt twelve of the thirteen cards.
Question: If the ace is currently in Player B's hand, Player A will win by switching hands. What are the chances that Player A will win by switching hands? Answer: Since the chances depend only on whether or not Player B originally got the ace, the chances are twelve out of thirteen.
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