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  • The Monty Hall Problem

    From Noel Whittaker's latest newsletter

    The contestant is faced with three doors. There is a new car behind one door and a goat behind each of the other two doors – the contestant has to choose the right door if they are to win the car. In the example given in the book, the contestant chooses a door, and before it is opened the compere opens one of the other two doors to reveal a goat. This means that the car is behind one of the remaining two doors.

    The compere then asks the contestant if he would like to switch from his original choice.

    This is the question – is he better off to stick with his original choice or switch? Most people will say he should stick with the original choice, but the correct answer is to switch. You see, the original choice had a two-thirds chance of being wrong, but now one door has been eliminated, the other door has a 50% chance of being right.

    Most people I discussed this with do not agree with the answer and will go to great lengths to tell you why the correct answer is wrong. Apparently this is such a famous puzzle that there is a large section devoted to it on Wikipedia.

    http://en.wikipedia.org/wiki/Monty_Hall_problem
    "There's one way to find out if a man is honest-ask him. If he says 'yes,' you know he is a crook." Groucho Marx

  • #2
    It's all about how the puzzle is posed according to the Wiki.

    IMO it's BS. Another classic example of how ststistics (probability in this case) can be skewed to suit whatever.
    Last edited by outspoken; 18-11-2008, 11:44 PM.

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    • #3
      Funnily enough I rented out a DVD tonight - 21, which deals with a group of university students counting numbers at the BlackJack Tables in Las Vegas.

      This car/goat example was used in the movie. "Apparently" the correct answer is to switch your choice.

      Hey, what do I know, I just watched the movie!!
      Patience is a virtue.

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      • #4
        It makes sense to me that a switch would increase your odds of geting it right.

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        • #5
          But then again Terry you think ( and spell) different to rest of us.

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          • #6
            lol.... I'm not sure if that's a good thing or not

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            • #7
              The reason it makes sense is that, after the first door is opened you now have more information than you did before, increasing the probability that your first choice was incorrect. Thus it makes sense to change your choice.
              DFTBA

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              • #8
                unless your first choice was right, then it makes no sense at all :-)

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                • #9
                  Originally posted by cube View Post
                  The reason it makes sense is that, after the first door is opened you now have more information than you did before, increasing the probability that your first choice was incorrect. Thus it makes sense to change your choice.
                  Cube- you've been listening to too many economists / commentators (like Bernard Hickey etc) who list their many useful numbers then jump to the conclusion that the world must be flat.

                  You have no more information about the 2 remaining doors than you did previously.
                  Sure, the probabilities have now changed from 1 in 3 to 1 in 2, but you still have zero information about either door, so there is no justification to choose one over the other.
                  Food.Gems.ILS

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                  • #10
                    If you chose the wrong door, then the compere is forced to open the only remaining door with a goat, giving a 100% chance that the remaining door conceals the car.

                    If you chose the right door, then the compere is able to open either remaining door without affecting the outcome.

                    So in the more likely scenario, where you chose the wrong door, there is now a 100% chance that the other door conceals the car.

                    It is an interesting problem, - one that I intuitively know is correct, but struggle to explain. Hopefully I'm getting better?

                    cube
                    DFTBA

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                    • #11
                      Statistically speaking you had a 1:3 chance originally behind every door. Now you have a 1:2 chance behind every door IT DOES NOT MATTER WHICH DOOR THE ODDS ARE THE SAME 2 doors 2 chances. However I would ask another question why did the compere open another door instead of your door. Did he know that your door had the car?
                      I would stick to the same door.
                      Doug

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                      • #12
                        according to the Wiki, the host doesn't know what is behind any of the doors?

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                        • #13
                          compere opens one of the other two doors to reveal a goat
                          It's not clear if this was by chance or inevitable.

                          Anyway, it doesn't matter - if s/he reveals a car, you lose anyway, and if its a goat, then the probability applies.
                          DFTBA

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                          • #14
                            Your doing a good job of explaining cube.
                            Mathmatically when the compere opens the door with a goat behind it the odd have not changed from 1in3 to 1in2. This is the bit that people get confused over which is why most people say, stay with the door you have already picked because you have a 50/50 chance.
                            I don't agree, since you have picked a door already, and lets assume its a door with a goat behind it, and now the compere has picked a door with a goat behind it, you now have a 100% chance of getting the right door if you change your door.
                            If you have already picked the right door, then you have a 100% chance of getting it wrong if you change.

                            Think of it like 2 people owning a poprerty together as tenants in common vs joint tenants.

                            In one each of you own 50% of the property and in the other each of you own 100% of the property.

                            You could also look at it this way.

                            When you first picked a door you had a 33% chance of getting the right door, which means you had a 66% chance of getting it wrong.

                            That means their is 66% chance that the car is behind the other 2 doors.

                            Now that the compere has opened one door and shown that a goat is behind that door it means that there is a 66% chance that the car is behind the other door.

                            Since you picked while the odd's where 33% chance it makes sense now to go for the 66% odd's which means you change doors.

                            Of course you can still get it wrong

                            How's that for warped.

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                            • #15
                              It is warped (apart from the spelling.....again :-) lol) because you're looking at the probability of getting it wrong.

                              When you first picked a door you had a 33% chance of getting the right door
                              agreed

                              Now that the compere has opened one door and shown that a goat is behind that door it means that there is a 66% chance that the car is behind the other door.
                              disagree
                              Now that the compere has opened one door and shown that a goat is behind that door it means that there is a 66% chance that the car is behind EITHER other door
                              you've forgotten about the fact that the car could be behind the door you originally chose, so the chance is now 50/50

                              Think of it like this....the probability adds up to 100% / 3 = 33%
                              but when you remove one of the wrong choices it becomes 100% / 2 = 50%

                              We could argue this forever & the wiki explains that the main arguement comes about by the way in which the puzzle is posed.

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