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  1. #21
    Super Moderator

    Join Date
    Dec 2006
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    East Lansing, MI
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    Re: the price is right

    Quote Originally Posted by LagerHead View Post
    I've read this problem many times. What I don't get is why the odds are 66% either way. In actuality you are only choosing between two doors since you will always be shown a zonker your only choices are ever your door and the remaining closed door. The third door is irrelevant in the problem except as a distraction.
    The third door is not irrelevant since you could have chosen that door in your original pick.

    The door that Monty shows after your pick is potentially based on which door you initially pick.

    If you pick the first zonker door, he shows you the second zonker door
    If you pick the second zonker door, he shows you the first zonker door
    If you pick the car door, he will show you either the first or second zonker door.

  2. #22
    ODN Community Regular

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    Jul 2008
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    Re: the price is right

    Quote Originally Posted by LagerHead View Post
    I've read this problem many times. What I don't get is why the odds are 66% either way. In actuality you are only choosing between two doors since you will always be shown a zonker your only choices are ever your door and the remaining closed door. The third door is irrelevant in the problem except as a distraction.
    Let me try a different approach to help you understand:

    Draw three doors on a piece of paper. Choose one (your door), circle it, and write "33% chance" above it. Now draw one big circle around the two other doors you didn't choose, with both inside the second circle. Write "66% chance" above that circle. These odds are correct, right?

    Monty shows you a goat behind one of the two other doors. Put an x on it, to eliminate it.

    The numbers above the circles don't change just because he shows you one of the doors. They don't, for example, change to 50% each. They stay the same at 33% and 66%, but the 66% chance is now concentrated on one door, instead of split between two. So, your odds of winning go up if you switch to the remaining door in the 66% circle.
    "If we lose freedom here, there is no place to escape to. This is the last stand on Earth." - Ronald Reagan

  3. #23
    Registered User

    Join Date
    Dec 2010
    Location
    northern ill noise
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    Re: the price is right

    try it for yourself
    http://www.mredkj.com/javascript/prob.html

    here were my results after a lot of clicking:
    120 total
    25 % correct when stay. (10 of 40)
    63 % correct when switch. (50 of 80)

 

 
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