A logic puzzle
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[Deleted User]
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Hello,
Here's an interesting puzzle:
There is a test subject and an experimenter and three closed boxes. One of the boxes has a $10.00 bill inside and the experimenter knows where it is. The subject doesn't, but if he can guess it correctly he can keep it. The subject picks one of the boxes and tells the experimenter. The experimenter opens one of the remaining two boxes (always an empty one) and asks the subject if he wants to now change his pick?
Should he do it and why?
Cheers, Ken
Here's an interesting puzzle:
There is a test subject and an experimenter and three closed boxes. One of the boxes has a $10.00 bill inside and the experimenter knows where it is. The subject doesn't, but if he can guess it correctly he can keep it. The subject picks one of the boxes and tells the experimenter. The experimenter opens one of the remaining two boxes (always an empty one) and asks the subject if he wants to now change his pick?
Should he do it and why?
Cheers, Ken
Post edited by [Deleted User] on
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No it's now 50/50!
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That's actually not true, specifically because the person running the experiment KNOWS which box is the correct one. You actually double your chances of winning by switching.
Rather than try and explain it myself, Google the "Monty Hall Problem."If you will it, dude, it is no dream. -
Yes, he should change his pick since one of the two remaining boxes was open leaving the one the subject picked and the other box that was empty. Therefore, the subject now knows which box has the money.
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Just give me the 10 bucks.
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Keep in mind the original box that the subject picked is still closed. He can either stay with that choice or jump to the other, unopened box.
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Still feel it's 50/50
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bobman1235 wrote: »That's actually not true, specifically because the person running the experiment KNOWS which box is the correct one. You actually double your chances of winning by switching.
Rather than try and explain it myself, Google the "Monty Hall Problem."
Thanks. There's a good illustration on wikipedia about it, I'd never think of it that way. The power of math;)AVR: H/K AVR240
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I agree...it's now a 50/50...I'd stay.
How can it be any other way?Most people just listen to music and watch movies. I EXPERIENCE them. -
Now I'm not sure
Monty Hall Problem.
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tony millard wrote: »I agree...it's now a 50/50...I'd stay.
How can it be any other way?
Think of it this way.
You're choosing one of three boxes. So when you pick your one box, there is a 1/3 chance you're correct, and a 2/3 chance it's one of the other two boxes, right?
Well, the person conducting the experiment knows which box is the correct one. He opens one that he KNOWS not to be the correct box. Your odds haven't changed - there was a 1/3 chance you were correct, and a 2/3 chance that it was one of the other two boxes. It's still a 2/3 chance that it's the one REMAINING box.
Tricky.If you will it, dude, it is no dream. -
When the subject picks one of the boxes he has a 1/3 chance of being correct. The remaining two boxes represent a 2/3 chance of being correct. Once the experimenter shows that one of the remaining boxes doesn't have the $10.00 the remaining box still represents a 2/3 chance, but concentrated in that single box. The original choice still has the 1/3 chance, so he should switch, every time. Having a 2/3 chance is better than a 1/3 chance.
The vast majority of people, who take this test, will always say remain with the original choice.
Ken -
Sorry, Bobman, while I was typing my response you were already posting.
Ken -
Kenneth Swauger wrote: »When the subject picks one of the boxes he has a 1/3 chance of being correct. The remaining two boxes represent a 2/3 chance of being correct. Once the experimenter shows that one of the remaining boxes doesn't have the $10.00 the remaining box still represents a 2/3 chance, but concentrated in that single box. The original choice still has the 1/3 chance, so he should switch, every time. Having a 2/3 chance is better than a 1/3 chance.
The vast majority of people, who take this test, will always say remain with the original choice.
Ken
Very interesting, thanks Ken. I would say it's not worth the headache for only 10$
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This puzzle was in a movie i watched fairly recently....I don't read the newsssspaperssss because dey aaaallllllllll...... have ugly print.
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I think what most people figure is that once one of the other two has been shown to not be the correct one, their odds go from 1 in 3 to 1 in 2. It started off with three boxes, now there are only two.
Many researchers feel that the way we view the world as a series of interrelated events. One action following another causes us to see the reduction of the number of boxes as changing the original odds.
Ken -
Kenneth Swauger wrote: »When the subject picks one of the boxes he has a 1/3 chance of being correct. The remaining two boxes represent a 2/3 chance of being correct. Once the experimenter shows that one of the remaining boxes doesn't have the $10.00 the remaining box still represents a 2/3 chance, but concentrated in that single box. The original choice still has the 1/3 chance, so he should switch, every time. Having a 2/3 chance is better than a 1/3 chance.
The vast majority of people, who take this test, will always say remain with the original choice.
Ken
Yes, the probability doesn't change to 50 after you find out cause your original choice was made before the box is revealed and thats where the biggest confusion is.AVR: H/K AVR240
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Kenneth Swauger wrote: »I think what most people figure is that once one of the other two has been shown to not be the correct one, their odds go from 1 in 3 to 1 in 2. It started off with three boxes, now there are only two.
Many researchers feel that the way we view the world as a series of interrelated events. One action following another causes us to see the reduction of the number of boxes as changing the original odds.
Ken
Haha beat me to itAVR: H/K AVR240
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I would open the box holding my gun. Then the test conductor gives the $10 and all the cash in his wallet as well!
Oh and BTW, technically that's not a logic question but a statistical odds question.Expert Moron Extraordinaire
You're just jealous 'cause the voices don't talk to you! -
And if you think THAT'S confusing, try figuring out the Birthday Paradox (not really a paradox, but it sounds cooler that way).In a group of at least 23 randomly chosen people, there is more than 50% probability that some pair of them will have the same birthday.... For 57 or more people, the probability is more than 99%If you will it, dude, it is no dream.
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sorry guys - the ability to reselect the box starts you off from a new slate. 1 out of 2 no matter how you slice it. People choose to keep the original box because there is nothing positive about the descision that would make them change thier mind - they are comparing one box to another matching box. In their minds their have already chosen the box, and putting it down to pick up the other one means twice the descision making cost ='s they have to select two boxes for the price of one.pop
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Ken, try this one.
There is a room. In that room are three lights. Each of those three lights is connected to one of three switches outside the room. The room has a door, but seals tight. You may only open the door and enter the room once, and you may only have one switch on when you do.
How can you tell which light goes to which switch?
Cheers,
RussCheck your lips at the door woman. Shake your hips like battleships. Yeah, all the white girls trip when I sing at Sunday service. -
sorry guys - the ability to reselect the box starts you off from a new slate. 1 out of 2 no matter how you slice it. People choose to keep the original box because there is nothing positive about the descision that would make them change thier mind - they are comparing one box to another matching box. In their minds their have already chosen the box, and putting it down to pick up the other one means twice the descision making cost ='s they have to select two boxes for the price of one.
You're right, all the statistics classes I've taken that have used this example were taught by idiots! Lumpy has revolutionized math!If you will it, dude, it is no dream. -
The movie was "21." Variable Change and all that jazz.I don't read the newsssspaperssss because dey aaaallllllllll...... have ugly print.
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Ken, try this one.
There is a room. In that room are three lights. Each of those three lights is connected to one of three switches outside the room. The room has a door, but seals tight. You may only open the door and enter the room once, and you may only have one switch on when you do.
How can you tell which light goes to which switch?
Cheers,
Russ
According to most building codes, the light switch closest to the entry point should be the one operating the lights inside the room.Expert Moron Extraordinaire
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When the contents of one of the boxes was exposed, the odds just changed. there is no 1/3 mystery placed on each box now. It's a 1/2 or 50% mystery now.;)bobman1235 wrote: »Think of it this way.
You're choosing one of three boxes. So when you pick your one box, there is a 1/3 chance you're correct, and a 2/3 chance it's one of the other two boxes, right?
Well, the person conducting the experiment knows which box is the correct one. He opens one that he KNOWS not to be the correct box. Your odds haven't changed - there was a 1/3 chance you were correct, and a 2/3 chance that it was one of the other two boxes. It's still a 2/3 chance that it's the one REMAINING box.
Tricky.Most people just listen to music and watch movies. I EXPERIENCE them. -
Ken the way my brain is scrambled these days, I would have subdued the tester and opened all the boxes for the $10, LOL!!!!
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I would open the box holding my gun. Then the test conductor gives the $10 and all the cash in his wallet as well!
Oh and BTW, technically that's not a logic question but a statistical odds question.
Statistics.;) that's what I say.
I picked one. didn't win...game over.
If I'm allowed to play again then the game should state in the beginning I have 2 tries and THEN it becomes a 2 out of 3 or 2/3rds chance of winning.
Funny, I use to loose no matter what, now I can not pay attention and win.
Except these Karmas on this forum:(Most people just listen to music and watch movies. I EXPERIENCE them. -
Ehhh....
The guy that showed you the box gives you the answer.
If he's going to show you a box, he won't show you yours off the bat, because then he wouldn't be able to let you change your mind anyways.
You have boxes A, B, and C.
You choose B.
He can't show you B, because then the scenario is all moot.
He shows you C, which doesn't have a box. He DOESN'T show you A for one of two reasons:
1) It has the item
2) Neither A nor C have the item, B does. We can't determine this right now.
Yes, there IS a 50% chance between the two remaining boxes, but looking at the bigger picture I.E. the THREE boxes, box A has the 2/3rds chance.I don't read the newsssspaperssss because dey aaaallllllllll...... have ugly print.
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That's a head scratcher, Russ. Let's see what I've come up with:
1). Let's number the switches 1,2 and 3 and the lights as A,B and C.
2). On a piece of paper I put 1, 2 and 3 at the tops of three columns. I placed an A, B and C underneath each column. Indicating that each switch could be connected to each of the lights.
3). If we throw switch 1 and look in the door and find light B lit we can cross off A and C from the 1 column. We can cross off B from column 2 and 3.
4). This is where I run out of logic steam. It seems to me that switch 2 could be connected to either light A or C. And the same can be said for switch 3, either A or C.
You only get one switch throw and one room look, so only one event can be known. I don't know.
Ken -
Ken, try this one.
There is a room. In that room are three lights. Each of those three lights is connected to one of three switches outside the room. The room has a door, but seals tight. You may only open the door and enter the room once, and you may only have one switch on when you do.
How can you tell which light goes to which switch?
Cheers,
Russ
I used to know that one.Now I don't..
I really love the one with 3 men splitting a hotel room, each pays something and later the clerk gives back some refund to one man and when he splits it up, a dollar dissapears. Now that was fun to tell in my younger years when we'd sit around for an hr. and laugh about it trying to rationalize while mentaly going in the other direction:DMost people just listen to music and watch movies. I EXPERIENCE them.
