Probability 101: Monty Hall

Probability 101: Monty Hall

This is a discussion on Probability 101: Monty Hall within the Off Topic & Humor Discussion forums, part of the The Back Porch category; Many of you know this already, so hold off for a minute (or a day) and let folks who have never heard it try to ...

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Thread: Probability 101: Monty Hall

  1. #1
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    Probability 101: Monty Hall

    Many of you know this already, so hold off for a minute (or a day) and let folks who have never heard it try to reason it out. I'll try to give a complete and clear explanation to start with...

    You are a contestant on Let's Make a Deal. You are given the opportunity to choose one of three doors - behind one is the Big Prize, behind the other two are goats. Assume that you want the Big Prize, and don't want a goat...

    You choose a door but, before Monty shows you if you've won, he opens one of the doors that you didn't choose, revealing a goat. He then gives you the option of staying with the door you originally chose, or switching to the last remaining door (the one you didn't choose and that he didn't open). What should you do?

    Caveat: This a pure probability question; assume that there is no way to gain any more information about what is behind either door. You must make your choice based only on the information provided.
    A man fires a rifle for many years, and he goes to war. And afterward he turns the rifle in at the armory, and he believes he's finished with the rifle. But no matter what else he might do with his hands - love a woman, build a house, change his son's diaper - his hands remember the rifle.


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    VIP Member Array friesepferd's Avatar
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    previously ur chances were 1:3, but now that he has gotten rid of a door, your chances are 1:2. your chances are 1:2 whether you switch doors or not.
    Wo die Notwehr aufhört, fängt der Mord an
    (Murder begins where self-defense ends)
    Georg Büchner

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    VIP Member Array Hiram25's Avatar
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    I'd stick with the door I chose. At least that way either win or lose it was my choice.

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    Goat tastes good, so its a win either way with me
    A real man loves his wife, and places his family as the most important thing in life. Nothing has brought me more peace and content in life than simply being a good husband and father.

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    Always..ALWAYS! Change from the door you picked to the other one. I was have this very discussion with my stats professor just the other day. You will win the car more often if you change doors.
    "The 280z, is more like a skittish, half broken bronco, that requires constant attention, challenges your driving ability and will literally ride the driver hard and put him away wet."
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    Member Array Mak9x18's Avatar
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    You should always switch.
    For those who understand, no explanation is necessary.
    For those who don't understand, no explanation is possible.


    John

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    VIP Member Array friesepferd's Avatar
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    Quote Originally Posted by Mak9x18 View Post
    You should always switch.
    why?
    Wo die Notwehr aufhört, fängt der Mord an
    (Murder begins where self-defense ends)
    Georg Büchner

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    VIP Member Array HKinNY's Avatar
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    Quote Originally Posted by Hiram25 View Post
    I'd stick with the door I chose. At least that way either win or lose it was my choice.
    +1. The odds are 50/50 either way. It is like driving on the highway no matter which lane you choose when you are in a rush is the wrong lane.

    I do not know how this will help with this problem, but my mother was on the Price Is Right and she won.

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    Senior Member Array Lewis128's Avatar
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    Quote Originally Posted by friesepferd View Post
    why?
    Of the three doors, if you pick a goat, Monty ALWAYS has to reveal the other goat.
    Since you don't know when you first pick, your odds are 1/3. Your odds of picking either goat are 2/3, so by switching doors you improve your odds.
    You are gambling that you picked a goat on your first try.

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    Does Monty really want you to walk out of there with the best prize?

    If he doesn't want you to win, and you happen to have chosen (to his knowledge) the big prize, then he might try to entice you from your sure thing, by reveling a door to you, and hoping that you'll change doors.

    OTOH, if he knows you chose a goat, and he doesn't want you to win, then why should he say anything.

    I never really trusted that Monty guy.
    Turn the election's in 2014 to a "2A Revolution". It will serve as a 1994 refresher not to "infringe" on our Second Amendment. We know who they are now.........SEND 'EM HOME. Our success in this will be proportional to how hard we work to make it happen.

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    Quote Originally Posted by HKinNY View Post
    I do not know how this will help with this problem, but my mother was on the Price Is Right and she won.
    It does not help... That's Bob Barker, this is Monty Hall. But always spay or neuter your pet!


    P.S. Give it up! What did she win? Inquiring minds want to know.
    -Bark'n
    Semper Fi


    "The gun is the great equalizer... For it is the gun, that allows the meek to repel the monsters; Whom are bigger, stronger and without conscience, prey on those who without one, would surely perish."

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    Member Array Mak9x18's Avatar
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    Lewis128 has it right. When you first select the chance is 1/3 for picking the winning door. If you select the winner then Monty can open either door. Your chances of selecting the goat are 2/3. If you do select the goat Monty has no choice; he has to open the other goat door. Your chance of winning goes to 2/3. If given the choice you should always switch.
    For those who understand, no explanation is necessary.
    For those who don't understand, no explanation is possible.


    John

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    VIP Member Array Hiram25's Avatar
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    Quote Originally Posted by HKinNY View Post
    +1. The odds are 50/50 either way. It is like driving on the highway no matter which lane you choose when you are in a rush is the wrong lane.

    I do not know how this will help with this problem, but my mother was on the Price Is Right and she won.
    HAVE YOU BEEN WATCHING ME DRIVE?

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    Distinguished Member Array Paymeister's Avatar
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    OK, help me here. I've had graduate courses in statistics. 'Course I also fell prey to the roulette wheel once, confusing a run with independent events. Sigh.

    But here, unless you're talking showmanship (that is, deducing things from the host's behavior), I can't see how your odds would be any different:
    • You had a 1/3 chance of winning on the first try. We all agree on that;
    • If he shows a goat behind an unchosen door, he's removed one 'bad choice';
    • He's left two options: one has the second goat, and one has the Big Prize;
    • You now have two choices (stay with your first door or switch to the other closed door);
    • Either choice is to choose ONE door out of TWO possibilities, = 50% likelihood of winning.

    How is switching beneficial?
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    I think he should spin the cylinder and then shoot. Oops, wrong logic puzzle!

    But I agree with Paymeister. If your odds are 1:2 of picking a correct option, how is that not 50%? The way I see it, the odds went from 33% to 50% after the first goat was revealed. So now, I either have a goat, or I don't.
    "Democracy is two wolves and a lamb voting on what to have for lunch; Liberty is a well-armed lamb contesting the vote."
    -- Benjamin Franklin

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