You are on a game show on television.

Discussion in 'Free Thoughts' started by Zarklephaser, Apr 24, 2006.

  1. Zarklephaser Registered Senior Member

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    186
    You are on a game show on television.

    On this game show the idea is to win a car as a prize.

    The game show host shows you three doors.

    He says that there is a car behind one of the doors and there are goats behind the other two doors.

    He asks you to pick a door.

    You pick a door but the door is not opened.

    Then the game show host opens one of the doors you didn't pick to show a goat (because he knows what is behind the doors).

    Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat.

    So he asks you if you want to change your mind and pick the other unopened door instead.

    What should you do?
     
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  3. Cottontop3000 Death Beckoned Registered Senior Member

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    Kick him in the nads and walk off.
     
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  5. James R Just this guy, you know? Staff Member

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    This is the "Monty Hall" problem, which has been discussed here before.

    Without answering, consider this:

    There are 100 doors instead of 3. Behind one is the car; behind 99 are goats. You choose number 57. The host of the show then opens 98 of the other doors, revealing goats. He then asks if you want to stick with door 57, or switch to the only other remaining door (number 23). What do you do?

    I know what I'd do...
     
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  7. Cottontop3000 Death Beckoned Registered Senior Member

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    Kick him in the nads and walk off?
     
  8. James R Just this guy, you know? Staff Member

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    No, I'd collect the car.
     
  9. Cottontop3000 Death Beckoned Registered Senior Member

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    What am I missing here? My brain? I knew I shouldn't have scrambled it.
     
  10. Athelwulf Rest in peace Kurt... Registered Senior Member

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    What's the point of this problem now? Is there a trick embedded in here somewhere?
     
  11. allisone417 i'll be in my room Registered Senior Member

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    yeah, something with percentages. read it before, and even then it was useless to me.
     
  12. Roman Banned Banned

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    If you choose one door out of 100, the chance of you getting a goat is 99%. You have a 1% chance of opening the door with the goat behind it. If you switch doors, you have a much higher chance of getting the car, as it's one door out of two, rather than 1 out of 100.
     
  13. Cottontop3000 Death Beckoned Registered Senior Member

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    Sure, but there is no reason to switch doors after he opens 98 of them, or one of them (in the op). You are faced with a new chance to choose, but the odds become the same for either door, regardless of what the odds were the first time around.

    Based on a 100 doors:

    Decision 1: 1% chance to find the car.
    Decision 2: 50% chance to find the car.

    Let's see.

    Decision one is really pointless, irrelevant. Any choice you make the first time around could be the car, but whether you pick the door with the car behind it this time around is meaningless, as you will be faced with a second decision where the odds will be 50% for either door, regardless of which door you picked the first time around.

    How could James R say he would collect the car?
     
  14. RubiksMaster Real eyes realize real lies Registered Senior Member

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    You have a higher chance of winning if you switch doors. There are 3 possible cases based on how you pick the initial door:

    1) you pick the car to begin with
    2) you pick a goat
    3) you pick the other goat

    Imagine you start with case 1. It's a 1/3 chance of happening. When Monty opens the other door, switching would reveal a goat. That is a LOSS.

    With case 2: Monty reveals the other goat. Switching would net you the car.

    With case 3: Monty reveals the other goat. Switching would net you the car.

    So TWO out of the three possible starting cases will get you the car if you switch doors. The only possible way you can lose on a switch is by picking the car to begin with. There's really no question about it. That is a 2/3 chance of winning the car when you switch doors. But if you didn't switch, you would only have a 1/3 chance of winning (i.e starting with case 1).
     
  15. Cottontop3000 Death Beckoned Registered Senior Member

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    2,959
    I see. The fact that he takes away a goat instead of the car after you make your first decision makes the difference. I'd still kick him in the nads and walk off. Ugghhhh. I hate this kind of problem. Something feels wrong about it, though. Can you put this into an equation for me, taking into account both decisions, where X is the probability of getting the car? It's been a long time since I took prob and stat.
     
    Last edited: Apr 24, 2006
  16. kaduseus melencolia I Registered Senior Member

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    statistically it's better to change your mind........but only when asked

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  17. RubiksMaster Real eyes realize real lies Registered Senior Member

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    I don't know enough about probability and statistics to do that, but Wikipedia has a pretty in-depth analysis of the problem: http://en.wikipedia.org/wiki/Monty_Hall_problem
     
  18. Cottontop3000 Death Beckoned Registered Senior Member

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    Thanks RubiksMaster. You were right. In the wikipedia article, under section 2.4, Bayes' Theorem, they explain it with an equation. I've always liked the fact that thoughts, like those in this thread, can be put into such equations. So, by switching doors, you have a 2/3 chance of getting the car.

    If you are doing the Quantum version of the paradox, which I understand even less, they say "you can do even better, and can sometimes even win the prize with certainty." Maybe that was what James R was referring to.
     
  19. Zarklephaser Registered Senior Member

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    Great thread, guys.
     
  20. Roman Banned Banned

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    You'd win and lose at the same time, and then physicists would make up a new particle, the goatton.
     
  21. draqon Banned Banned

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    well the simple answer is: I am not on that game show...so this all doesnt apply. I dont want to spend neurons for cars or goats, cause anticipation is stress and stress is neurons death
     
  22. Roman Banned Banned

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    A goat wouldn't be so bad. A little stringy, a little gamey, but hey, free food is free food.
     
  23. spuriousmonkey Banned Banned

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    What kind of car is it?
     

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