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| 8 JAN 2003 at 9:57pm |
Agustín CordesGuild Master
Posts : 5696
Joined: 23 OCT 2002
Location: AR, Buenos Aires
Status : Offline | 1) 3 revolutions
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| 8 JAN 2003 at 10:03pm |
Agustín CordesGuild Master
Posts : 5696
Joined: 23 OCT 2002
Location: AR, Buenos Aires
Status : Offline | 2) In the first place you have a 33% chance of chosing the right door. After the host opens a wrong door, you have 50% chance of chosing the right door. It doesn't really matters if you change your choice or not.
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| 8 JAN 2003 at 10:32pm |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By Rael (8 JAN 2003 10:02pm)
2) In the first place you have a 33% chance of chosing the right door. After the host opens a wrong door, you have 50% chance of chosing the right door. It doesn't really matters if you change your choice or not.
Here's an alternate explanation: in the first round, you have a 1/3 (not exactly 33%) chance of choosing the right door. In the second round, there is 66% chance that the door you didn't choose is the right one, hence you should change your choice.
Let me explain. Suppose we label the doors A, B, C. Any of them can be the prize door with equal probability. Let's say the first choice is always A and second choice is whichever of B, C is left.
There is 1/3 probability that A was the right one and you will erroneously switch away from it. However, there is 2/3 probability that the right door is B or C and you will get the right one.
So yes, you should switch and yes, it does matter.
I forgot my sig.
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| 8 JAN 2003 at 10:45pm |
Agustín CordesGuild Master
Posts : 5696
Joined: 23 OCT 2002
Location: AR, Buenos Aires
Status : Offline | Originally Posted By MichalN (8 JAN 2003 10:32pm)
(not exactly 33%)
You're right, it's 33.3333333333333333333...%
Anyway, I liked your explanation better.
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| 9 JAN 2003 at 12:00am |
InlandAZGuild Master
Posts : 5587
Joined: 4 MAY 2007
Status : Offline | Here's an alternate explanation: in the first round, you have a 1/3 (not exactly 33%) chance of choosing the right door. In the second round, there is 66% chance that the door you didn't choose is the right one, hence you should change your choice.
Seems to me that's it a only 50 % chance - once the other door is revealed to be empty -
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| 9 JAN 2003 at 12:41am |
AyaGrand Inquisitor
Posts : 7277
Joined: 16 OCT 2002
Status : Offline | Originally Posted By MichalN (8 JAN 2003 10:32pm)
So yes, you should switch and yes, it does matter.
no it doesn't matter! at first you got 1 out of 3 probability to get it right... when one of the wrong doors is opened then there's a 1/2 probability that you chose the right door... whether you change your selection is not at all important, the probability will still be 1/2
You have gotten the attention of the mysterious lady. She turns to face you. Her face is devoid of any flesh. You are frozen with horror as she begins ripping your body into a bloody mess.
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| 9 JAN 2003 at 12:51am |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By Aya_Brea (9 JAN 2003 12:41am)
no it doesn't matter! at first you got 1 out of 3 probability to get it right... when one of the wrong doors is opened then there's a 1/2 probability that you chose the right door...
No. If you don't change your selection, the probability stays at 1/3.
whether you change your selection is not at all important, the probability will still be 1/2
I beg to differ. We'll see whar the arbiter (szcax) has to say but I still think what I said was right.
What you are forgetting is that you are receiving extra information about the two doors you didn't choose initially.
I say that the probabilities of getting the prize are like this:
- Choose one and stick with that selection - 1/3
- Choose one and randomly choose another - 1/2
- Choose one and then the other - 2/3
I think we all agree on the first two.
There is 2/3 chance you got the initial choice wrong. However, if you were indeed wrong the first time (and there is 2/3 probability you were!), you will be right the second time, turning the disadvantage into your advantage.
I forgot my sig.
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| 9 JAN 2003 at 12:55am |
Agustín CordesGuild Master
Posts : 5696
Joined: 23 OCT 2002
Location: AR, Buenos Aires
Status : Offline | Originally Posted By MichalN (9 JAN 2003 12:51am)
What you are forgetting is that you are receiving extra information about the two doors you didn't choose initially.
Uh-oh, I think I see a problem in your logic becuase you do choose one of the remaining doors initially. Read carefuly.
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| 9 JAN 2003 at 12:58am |
szcaxJourneyman
Posts : 935
Joined: 12 OCT 2002
Status : Online | Originally Posted By MichalN (9 JAN 2003 12:51am)
I beg to differ. We'll see whar the arbiter (szcax) has to say but I still think what I said was right.
And interfere with this great squabble? I think not! I'll let people mull about until tommorrow. Don't forget, the answer to the first one hasn't been figured out yet. It's not 3
Black holes are where God divided by zero
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| 9 JAN 2003 at 1:04am |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By szcax (9 JAN 2003 12:58am)
And interfere with this great squabble?
Scientific discourse you mean?
Don't forget, the answer to the first one hasn't been figured out yet. It's not 3
Maybe the question was formulated ambiguously. Revolutions around which axis?
I forgot my sig.
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| 9 JAN 2003 at 1:26am |
AyaGrand Inquisitor
Posts : 7277
Joined: 16 OCT 2002
Status : Offline | the probabilities change according to the sample... no matter how many doors there are (x) you'll have 1/x chance to get it right... if some of the wrong doors are revealed (y) and you get to guess again, no matter what you guess, your probability will now be 1/x-y... if you don't guess again it doesn't matter which and how many doors are opened, you always have 1/x chance to get it right
You have gotten the attention of the mysterious lady. She turns to face you. Her face is devoid of any flesh. You are frozen with horror as she begins ripping your body into a bloody mess.
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| 9 JAN 2003 at 1:29am |
AyaGrand Inquisitor
Posts : 7277
Joined: 16 OCT 2002
Status : Offline | on this specific example the question "Now that you know door one is a dud, you may switch to door number three. Would you like to?" is a trick question... when this question is uttered it can immediately be translated as "Now that you know door one is a dud, which door do you want, 2 or 3?" answering no to the first is like answering 2 to the second, answering yes is like answering 3... so your probability changes to 1/2
You have gotten the attention of the mysterious lady. She turns to face you. Her face is devoid of any flesh. You are frozen with horror as she begins ripping your body into a bloody mess.
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| 9 JAN 2003 at 1:54am |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By Aya_Brea (9 JAN 2003 1:25am)
the probabilities change according to the sample... no matter how many doors there are (x) you'll have 1/x chance to get it right... if some of the wrong doors are revealed (y) and you get to guess again, no matter what you guess, your probability will now be 1/x-y... if you don't guess again it doesn't matter which and how many doors are opened, you always have 1/x chance to get it right
Exactly! The point is, I'm saying you shouldn't guess the second time and should choose a door other than your initial selection. Then there is ((x-1)/(x))*(1/(x-y-1)) probability of success, instead of 1/x. I think
Which for x=3 and y=1 works out to 2/3. For x=4 and y=1 it would be 0.375 which is still better than 0.25.
I forgot my sig.
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| 9 JAN 2003 at 2:06am |
AyaGrand Inquisitor
Posts : 7277
Joined: 16 OCT 2002
Status : Offline | but whichever door you choose the second time it will be 1 door out of 2... if you say you'll stick to your selection it's 1/(3-1)... if you say you'll change your choise again it's 1/(3-1)... both are an entirely new selection with a new sample
according to your example if there were 100 doors and the host opened 98 then if you changed your selection you'd have a 0.99 probability to be right when selecting 1 out of 2!!! of course not... 1 out of 2 is always 0.5
You have gotten the attention of the mysterious lady. She turns to face you. Her face is devoid of any flesh. You are frozen with horror as she begins ripping your body into a bloody mess.
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| 9 JAN 2003 at 2:27am |
szcaxJourneyman
Posts : 935
Joined: 12 OCT 2002
Status : Online | Originally Posted By MichalN (9 JAN 2003 1:04am)
Revolutions around which axis?
The question is asking how many times the smaller circle will make a complete rotation (If it's a quarter, one rotation would mean our friend George Washington did one somersault) before it gets to its initial point on the large circle.
Black holes are where God divided by zero
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| 9 JAN 2003 at 2:46am |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By Aya_Brea (9 JAN 2003 2:05am)
but whichever door you choose the second time it will be 1 door out of 2... if you say you'll stick to your selection it's 1/(3-1)... if you say you'll change your choise again it's 1/(3-1)... both are an entirely new selection with a new sample
No! I'm saying that the second time you randomly choose a door other than the one you selected first. In case of three door, there is only one such door so the second selection isn't very random at all.
according to your example if there were 100 doors and the host opened 98 then if you changed your selection you'd have a 0.99 probability to be right when selecting 1 out of 2!!! of course not... 1 out of 2 is always 0.5
Of course yes! If you randomly select one of the remaining doors then yes, there is 1/2 chance of success.
BUT! There is 99% chance that your initial selection was wrong, ie. one of the 99 doors you didn't choose contains the prize. And it that case, there is 99% chance (overall) that the other remaining door is the right one.
You seem to be overlooking the fact that there are two selections going on and for the second one you've received extra information.
I forgot my sig.
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| 9 JAN 2003 at 2:48am |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By szcax (9 JAN 2003 2:27am)
The question is asking how many times the smaller circle will make a complete rotation (If it's a quarter, one rotation would mean our friend George Washington did one somersault) before it gets to its initial point on the large circle.
That is not a very clear answer... So I will be more explicit. Are you asking about rotation around the axis of the smaller circle, the larger circle or both?
Of course, this question may be the answer
I forgot my sig.
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| 9 JAN 2003 at 3:01am |
szcaxJourneyman
Posts : 935
Joined: 12 OCT 2002
Status : Online | Ok I think I see what you mean.... the big circle is totally still. The question is asking how many times the small circle rotates around it's own axis as it rolls around the circumference of the big circle...
Black holes are where God divided by zero
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| 9 JAN 2003 at 3:09am |
Agustín CordesGuild Master
Posts : 5696
Joined: 23 OCT 2002
Location: AR, Buenos Aires
Status : Offline | Originally Posted By szcax (9 JAN 2003 3:00am)
Ok I think I see what you mean.... the big circle is totally still. The question is asking how many times the small circle rotates around it's own axis as it rolls around the circumference of the big circle...
Unless my understanding of English is mistaken due to my lack of sleep, it's still three revolutions - the circumference of the big circle is three times the circumference of the small circle.
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| 9 JAN 2003 at 3:15am |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By Rael (9 JAN 2003 3:09am)
Unless my understanding of English is mistaken due to my lack of sleep, it's still three revolutions - the circumference of the big circle is three times the circumference of the small circle.
That's what I'd say too. Three times around its own axis and once around the axis of the larger circle (obviously).
I forgot my sig.
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| 9 JAN 2003 at 4:07am |
InlandAZGuild Master
Posts : 5587
Joined: 4 MAY 2007
Status : Offline | I'm confused (SNAFU) -
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| 9 JAN 2003 at 5:57am |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By InlandAZ (9 JAN 2003 4:07am)
I'm confused (SNAFU) -
Confused by what exactly? I dare say there's a lot to be confused by in this thread Or are you just generally confused?
I forgot my sig.
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| 9 JAN 2003 at 1:17pm |
AyaGrand Inquisitor
Posts : 7277
Joined: 16 OCT 2002
Status : Offline | Originally Posted By MichalN (9 JAN 2003 2:46am)
Of course yes! If you randomly select one of the remaining doors then yes, there is 1/2 chance of success.
BUT! There is 99% chance that your initial selection was wrong, ie. one of the 99 doors you didn't choose contains the prize. And it that case, there is 99% chance (overall) that the other remaining door is the right one.
You seem to be overlooking the fact that there are two selections going on and for the second one you've received extra information.
practically you might be right i think... i see your point... it's more obvious with 100 doors than it is with 3! but mathematically i think you're wrong cause the probability during the second choice is 1/2 cause it's a separate choice... but when you're based to the fact that your first choice was 99% wrong (or 66% for the 3 doors) then yes you theoretically have a bigger chance if you change your selection
You have gotten the attention of the mysterious lady. She turns to face you. Her face is devoid of any flesh. You are frozen with horror as she begins ripping your body into a bloody mess.
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| 9 JAN 2003 at 6:58pm |
MichalNGrand Inquisitor
Posts : 7058
Joined: 14 SEP 2003
Status : Online | Originally Posted By Aya_Brea (9 JAN 2003 1:17pm)
practically you might be right i think... i see your point... it's more obvious with 100 doors than it is with 3!
Aha! Yes, the 100 door example seems clearer. Thanks for coming up with it
but mathematically i think you're wrong cause the probability during the second choice is 1/2 cause it's a separate choice...
Only if you disregard what you know about the doors. If you randomly choose from the remaining two doors then there's no question, the chance of success is 50%. What I'm saying is that the second choice should not be random at all.
but when you're based to the fact that your first choice was 99% wrong (or 66% for the 3 doors) then yes you theoretically have a bigger chance if you change your selection
Exactly.
I forgot my sig.
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