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Thread: Puzzle #1

  1. #1
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    Default Puzzle #1

    Imagine you are a contestant on a US game show. You have the chance to win a Rolls-Royce (or a Porsche).

    There are three doors, and you must choose one. The Rolls is behind one of the doors; there are goats behind the other two.

    You choose one door, let's call it A. but you don't open it. The hostólet's call him Montyóchooses another, say B, and opens it; there is a goat there.

    Now it's your turn to open a door. Monty asks if you want to stick with your original choice A, or if you want to change and open the third door, C.

    So, should you go for A or C? And why?

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  3. #2
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    Too early in the morning for a quiz!My brain hasn't woken up yet!

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    Quote Originally Posted by Empirical View Post
    ... The hostólet's call him Montyóchooses another, say B, and opens it; there is a goat there.

    ...

    Let's call him Monty Hall

    http://puzzles4you.blogspot.ie/2009/...hall-trap.html

    It's a great puzzle. When I'm selling stuff I'll give people 2 choices and they choose the second one 99% of the time.

    Just like when you're Q-ing at a bar, the guy in front will take his drinks and 99% turn to the left, so be at his right elbow and you'll get into the space quicker than the guy Q-ing at his left elbow.

    Mmmm-hmm




  5. #4

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    Quote Originally Posted by Empirical View Post
    Imagine you are a contestant on a US game show. You have the chance to win a Rolls-Royce (or a Porsche).

    There are three doors, and you must choose one. The Rolls is behind one of the doors; there are goats behind the other two.

    You choose one door, let's call it A. but you don't open it. The host—let's call him Monty—chooses another, say B, and opens it; there is a goat there.

    Now it's your turn to open a door. Monty asks if you want to stick with your original choice A, or if you want to change and open the third door, C.

    So, should you go for A or C? And why?
    I would change to C. The odds were 2-1 against me getting it right first time. For some reason it has been proven that although the odds are now evens by changing you have a better chance. Saw something like this on Derren Brown.

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    Quote Originally Posted by The kraut View Post
    I would change to C. The odds were 2-1 against me getting it right first time. For some reason it has been proven that although the odds are now evens by changing you have a better chance. Saw something like this on Derren Brown.
    Cant say I get that. There are three doors. You know nothing about what is behind any door. You pick one at random. One of the doors you didn't choose turns out to have goats behind it, so your chances of having picked the correct door have gone up from one in three to one in two. But you have learnt nothing additional about what is behind either A or C.

    Therefore I suggest that as between A and C it is irrelevant that B had goats behind it. But it is also irrelevant that you previously picked A. After B has been opened, the game - effectively - starts again: you have two doors, behind one is the car behind the other is the goat. You have to choose one door at random, you have a fifty/fifty chance of being correct. Therefore choosing either A or C the second time around is equally rational.

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  8. #6
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    You should always change....................
    Lets assume there were ten doors and behind nine there is nothing..................behind one there is a car.
    You pick number six.........................you have a one in ten chance of being correct.
    Now the host (Monty Hall) removes eight leaving number four.......................he cannot remove the door that has the car behind it.

    Now your number six is still only a one in ten chance of being right and the other door is a NINE in ten chance of being right.

    It is not fifty/fifty although there are only two cards left.

    So which door is is probably best to open? the one offered by the host.

    Magicman
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    Respect ................ obvious when given................. and so obvious when not given.
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    I would have walked by that point. Not the girl in the photos

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    Quote Originally Posted by samlad View Post
    I would have walked by that point. Not the girl in the photos
    My god - I hope a goat never opens the door
    Seek and you shall find!

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    Quote Originally Posted by UB40 View Post
    My god - I hope a goat never opens the door
    I've woken up next to worse

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    Quote Originally Posted by Magicman View Post
    Now your number six is still only a one in ten chance of being right and the other door is a [B]NINE in ten chance of being right
    Don't think so. The removal of the other eight doors changes the chances of the door you have chosen being the correct one. The chances of that are now 50/50.

    Probability is the ratio of favourable outcomes to total outcomes. What the deletion of the other eight doors has done is to change the total number of possible outcomes from 10 to 2. Your choice is still one, but it has gone from 1:10 to 1:2.
    Last edited by Dr. Ivory; 03-08-14 at 15:39.

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