Page 1 of 6 12345 ... LastLast
Results 1 to 15 of 80
  1. #1
    Prospect
    Points: 5,284, Level: 21
    Level completed: 47%, Points required for next Level: 266
    Overall activity: 1.0%
    Achievements:
    Veteran5000 Experience Points

    Join Date
    Jan 2008
    Posts
    31
    Points
    5,284
    Level
    21
    Thumbs Up
    Received: 2
    Given: 0

    Lets make a deal!

    I had so much fun reading the thread on the plane that I thought I would introduce a puzzle that provokes the same kind of debate.

    I introduced it to some young co-workers who were grads of Carleton College, a liberal arts school with a reputation for strong academics. One rolled his eyes, came up with the right answer, three others quickly understood the right answer, and the fourth was adamant that I was wrong, that my calculations were wrong, and that my computer simulation was wrong.

    When I saw the discussion in a science fiction magazine, someone with an advanced science degree of some sort who used statistics as a normal part of his work blew his explanation because of a particular fallacy that many people make, sort of like the perception that wheel speed restricts the forward speed of an aeroplane on a treadmill.

    Let's say you are a contestant on a game show. The host, I’ll call him Monty, has three boxes on stage. One has a valuable prize, the other two contain (pygmy) goats. You make your choice, Monty brings the box to you, and the other two boxes remain on stage. Of course, at least one of the boxes still on stage contains a goat. Monty deliberately chooses a box containing a goat and the box is opened to show you the goat.

    So, now you have your box, there is a box on stage. One of these two boxes contains a prize, the other a goat. At this point, you can switch boxes if you wish. What do you do? Does it make any difference?

    My rules:
    The math needed to solve this problem is elementary probability. I got enough in a survey course on discrete (integer only) math in computer science. You can also exhaustively examine all the possible cases and see how many win. There are only a dozen cases, if my memory and math serve me correctly. You are welcome to solve the problem analytically. However, explain the answer logically without reference to the math involved, or even whether or not the problem was solved analytically. You are trying to convince someone who’s knowledge of probability is only enough to realize that there is a 1/3 chance of a box containing a prize, and a 2/3 chance of a box containing a goat.
    dirty dick


    Last edited by keepngoal; 02-01-2008 at 11:54 AM.

  2. #2
    Addict
    Points: 132,856, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Overall activity: 6.0%
    Achievements:
    SocialYour first GroupVeteranCreated Album pictures50000 Experience Points
    cyismydog's Avatar
    Join Date
    Apr 2006
    Posts
    6,353
    Points
    132,856
    Level
    100
    Thumbs Up
    Received: 14
    Given: 10

    Re: Lets make a deal!

    Pick the other box, because you have a 50% chance of being right. It's not really common sense, but it works out mathematically. I saw it on an episode of numb3rs.



  3. #3
    Walk On
    Points: 9,097, Level: 28
    Level completed: 58%, Points required for next Level: 253
    Overall activity: 0%
    Achievements:
    Veteran5000 Experience Points

    Join Date
    Apr 2007
    Location
    East of Omaha
    Posts
    192
    Points
    9,097
    Level
    28
    Thumbs Up
    Received: 0
    Given: 0

    Re: Lets make a deal!

    Can I smell the box?



    Make the switch (I'm a stat major so I'll wait to explain).



  4. #4
    Prospect
    Points: 5,284, Level: 21
    Level completed: 47%, Points required for next Level: 266
    Overall activity: 1.0%
    Achievements:
    Veteran5000 Experience Points

    Join Date
    Jan 2008
    Posts
    31
    Points
    5,284
    Level
    21
    Thumbs Up
    Received: 2
    Given: 0

    Re: Lets make a deal!

    You buy them books, and buy them books, all they do is eat the pages. Your answer is to be without reference to a mathematical solution. There is an error in the previous post.



  5. #5
    All-Star
    Points: 27,686, Level: 51
    Level completed: 13%, Points required for next Level: 964
    Overall activity: 10.0%
    Achievements:
    Veteran25000 Experience Points
    ahaselhu's Avatar
    Join Date
    Sep 2007
    Location
    Boone, IA
    Posts
    1,785
    Points
    27,686
    Level
    51
    Thumbs Up
    Received: 6
    Given: 30

    Re: Lets make a deal!

    Quote Originally Posted by BurgundyClone View Post
    Can I smell the box?



    Make the switch (I'm a stat major so I'll wait to explain).
    Agreed, but I'll let the stat major explain



  6. #6
    Prospect
    Points: 5,284, Level: 21
    Level completed: 47%, Points required for next Level: 266
    Overall activity: 1.0%
    Achievements:
    Veteran5000 Experience Points

    Join Date
    Jan 2008
    Posts
    31
    Points
    5,284
    Level
    21
    Thumbs Up
    Received: 2
    Given: 0

    Re: Lets make a deal!

    Sorry, am not used to the instant feedback. cyismydog's reply



  7. #7
    Hall-Of-Famer
    Points: 76,419, Level: 85
    Level completed: 93%, Points required for next Level: 131
    Overall activity: 1.0%
    Achievements:
    SocialVeteranCreated Album pictures50000 Experience Points
    4429 mcc's Avatar
    Join Date
    Aug 2007
    Location
    Wall Street
    Posts
    4,402
    Points
    76,419
    Level
    85
    Thumbs Up
    Received: 1
    Given: 0

    Re: Lets make a deal!

    Quote Originally Posted by rdtindsm View Post
    You buy them books, and buy them books, all they do is eat the pages. Your answer is to be without reference to a mathematical solution. There is an error in the previous post.
    Quote Originally Posted by rdtindsm View Post
    Sorry, am not used to the instant feedback. cyismydog's reply
    Man this one is tuff as rain.



  8. #8
    Addict
    Points: 84,468, Level: 90
    Level completed: 40%, Points required for next Level: 1,082
    Overall activity: 2.0%
    Achievements:
    Veteran50000 Experience PointsSocial
    cstrunk's Avatar
    Join Date
    Mar 2006
    Location
    Longview, TX
    Posts
    8,107
    Points
    84,468
    Level
    90
    Thumbs Up
    Received: 25
    Given: 2

    Re: Lets make a deal!

    Quote Originally Posted by cyismydog View Post
    Pick the other box, because you have a 50% chance of being right. It's not really common sense, but it works out mathematically. I saw it on an episode of numb3rs.
    If there are only two boxes left... don't you have the same 50% chance that the box you are holding has the prize? I don't see the reason to switch.

    I hate statistics.



  9. #9
    Hall-Of-Famer
    Points: 38,432, Level: 60
    Level completed: 49%, Points required for next Level: 618
    Overall activity: 4.0%
    Achievements:
    Veteran25000 Experience Points
    cloneu's Avatar
    Join Date
    Jul 2007
    Location
    Twin Cities
    Posts
    4,144
    Points
    38,432
    Level
    60
    Thumbs Up
    Received: 17
    Given: 15

    Re: Lets make a deal!

    I assume I would pick the goat first, as I always pick the wrong thing. So I would switch. But maybe I would switch and get the goat because that is my bad luck. I think I saw this debate in the Princess Diaries. I would switch. If nothing else I would get a lawn mower out of the deal.


    Step 1: Cut a hole in the box.

  10. #10
    Starter
    Points: 13,878, Level: 35
    Level completed: 76%, Points required for next Level: 172
    Overall activity: 1.0%
    Achievements:
    Veteran10000 Experience Points

    Join Date
    Apr 2006
    Posts
    684
    Points
    13,878
    Level
    35
    Thumbs Up
    Received: 0
    Given: 0

    Re: Lets make a deal!

    I'm an English major so I assume I can try. Stats majors are just cheating... :)

    The way I think of it is that there is a 33% chance you were right the first time, and a 66% chance you were wrong. By eliminating one of the two other choices, one assumes the probability of the other and so you should switch from your original choice.

    Think of it with 100 choices. There is a 1% chance you were right. If the host took away 98 of the 99 that you didn't pick, and then asked you if you wanted to switch, of course you would. In fact, even if he took away 1 choice I think it would still be smart to switch because now you would be picking out of 99 instead of 100. I think...


    have you ever got caught outside In a strong rainfall? Yes or NO. If it"s yes, then you might half felt the pane of hard(tought) rain on you head. If it hurt"s then it"s tough. Yes or no. Okay I'm right and you know it.

    So alothough you attempt"ed to say you didn"t understnad, now you do. Fair enough?

  11. #11
    Addict
    Points: 59,640, Level: 75
    Level completed: 73%, Points required for next Level: 410
    Overall activity: 1.0%
    Achievements:
    SocialVeteran50000 Experience Points
    guitarchitect7's Avatar
    Join Date
    Oct 2006
    Posts
    6,318
    Points
    59,640
    Level
    75
    Thumbs Up
    Received: 0
    Given: 1

    Re: Lets make a deal!

    Quote Originally Posted by markshir View Post
    I'm an English major so I assume I can try. Stats majors are just cheating... :)

    The way I think of it is that there is a 33% chance you were right the first time, and a 66% chance you were wrong. By eliminating one of the two other choices, one assumes the probability of the other and so you should switch from your original choice.

    Think of it with 100 choices. There is a 1% chance you were right. If the host took away 98 of the 99 that you didn't pick, and then asked you if you wanted to switch, of course you would. In fact, even if he took away 1 choice I think it would still be smart to switch because now you would be picking out of 99 instead of 100. I think...
    I like this explaination. I never took stats, so logical thinking gets me here.


    "You must try to generate happiness within yourself. If you aren't happy in one place, chances are you won't be happy anyplace." -- Ernie Banks



  12. #12
    Prospect
    Points: 5,799, Level: 22
    Level completed: 50%, Points required for next Level: 251
    Overall activity: 0%
    Achievements:
    Veteran5000 Experience Points

    Join Date
    Feb 2007
    Location
    Des Moines
    Posts
    35
    Points
    5,799
    Level
    22
    Thumbs Up
    Received: 0
    Given: 0

    Re: Lets make a deal!


  13. #13
    Legend
    Points: 205,370, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Overall activity: 13.0%
    Achievements:
    Veteran50000 Experience Points
    jbhtexas's Avatar
    Join Date
    Oct 2006
    Location
    Arlington, TX
    Posts
    10,748
    Points
    205,370
    Level
    100
    Thumbs Up
    Received: 145
    Given: 91

    Re: Lets make a deal!

    Quote Originally Posted by rdtindsm View Post
    Let's say you are a contestant on a game show. The host, Iíll call him Monty, has three boxes on stage. One has a valuable prize, the other two contain (pygmy) goats. You make your choice, Monty brings the box to you, and the other two boxes remain on stage. Of course, at least one of the boxes still on stage contains a goat. Monty deliberately chooses a box containing a goat and the box is opened to show you the goat.

    So, now you have your box, there is a box on stage. One of these two boxes contains a prize, the other a goat. At this point, you can switch boxes if you wish. What do you do? Does it make any difference?
    Am I told before hand that there are two goats and one nice prize?

    If so, I know that no matter which box I pick, there will be at least one goat left on stage. So, Monty deliberately opening a box with a goat and showing me what I already know to be true would seem to be rather irrelevant in deciding whether I should switch boxes.

    So, with the TV drama out of the way, with two boxes left I have a 50-50 chance of picking the prize. My box stands just as good a chance of having the prize as the one left on stage.


    "Don't worry Boss...they can't do nothin' 'til they're through sparklin'..."

    Avatar - America's new superhero...Cenex Guy

  14. #14
    Prospect
    Points: 5,284, Level: 21
    Level completed: 47%, Points required for next Level: 266
    Overall activity: 1.0%
    Achievements:
    Veteran5000 Experience Points

    Join Date
    Jan 2008
    Posts
    31
    Points
    5,284
    Level
    21
    Thumbs Up
    Received: 2
    Given: 0

    Re: Lets make a deal!

    Maybe I should let this keep going, but markshir is correct, and the reasoning I was looking for. He is almost brilliantly obscure in his insight, similar to collapsing wave functions in quantum theory and the Schroedenger cat analogy.

    Many people will say it doesn't matter. They see two boxes and think the probability is 50 - 50. They are looking at the problem as a new one. Anyone entering the studio will see two boxes and they would indeed have a 50% chance of choosing the right box.

    But the initial chance of the prize being on stage is 2/3. Nothing that you do later affects this. You merely know that if the prize is on stage, it is in the remaining box.

    A slightly mathematical explanation is: If the prize is onstage (p = 2/3), the probablility of the prize being in the 2nd box is one for a total probability of 2/3.

    Let me share a cartoon with you. I first saw this as part of an animation festival at the Union that was presented probably about 1970. It doesn't strike you as being particularly funny at first, but it is the only one I remember, and in fact as been voted to a top 50 list by other animators.

    [ame="http://www.youtube.com/watch?v=BXCUBVS4kfQ"]YouTube - Bambi Meets Godzilla[/ame]


    Last edited by rdtindsm; 02-01-2008 at 01:33 PM.

  15. #15
    Addict
    Points: 82,670, Level: 89
    Level completed: 40%, Points required for next Level: 1,080
    Overall activity: 1.0%
    Achievements:
    Veteran50000 Experience Points
    CYVADER's Avatar
    Join Date
    Nov 2006
    Location
    Cornfields
    Posts
    5,231
    Points
    82,670
    Level
    89
    Thumbs Up
    Received: 11
    Given: 5

    Re: Lets make a deal!

    what the hell just happened?



Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
  • TV: Fox Sports 1
  • Iowa State vs. North Dakota State
  • August 30, 2014
  • 11:00 AM