That can't be right. Think about it. You choose one door out of three so you have a 1/3 chance. You're saying this increases to 1/2 because the host opens a door???jens wrote:even if you stay with your original choice you actively choose if you're being asked for the second timefabi the underachiever wrote:yay, so proud of myself again... i may be wrong, but it just seems so intuitive, no matter what they say.
am i kind of right that if you stay put, chances are 33%, and if you change your mind they are 50%?
would only make sense, because if you change your mind, you essentially change the setup - i.e. you do not choose from one out of three, but from one out of two. and it is very clear, that the one has odds of a third, and the other of a half...
but this is all just erm... my mind rambling... yay.
door1 -> 33%
door2 -> 33%
door3 -> 33%
you choose door1 and door 2 is opened and there's a goat
now you have a new choice:
wanna stay with your original choice = door1
wanna change your choice = door3
and your chances are:
door1=50%
door3=50%
thus whatever you choose your chances are 50%
er... I think
YOU WILL NOT BELEIVE THIS
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- KVRer
- 28 posts since 21 Oct, 2005
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- KVRAF
- 1817 posts since 1 Jun, 2003
you got lucky that i don't need to ask you where you rrrreside...putte wrote:.. pure magic! ..jens wrote:and so am I ...fabi the underachiever wrote: I am drunk
erm, i think i'll call friends in the US now. feel talkative...
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- KVRAF
- 1577 posts since 20 May, 2002 from Cambridge, UK
that's it exactly - told you it was counter-intuitive!Bob Gravy wrote: That can't be right. Think about it. You choose one door out of three so you have a 1/3 chance. You're saying this increases to 1/2 because the host opens a door???
THIS IS MY MUSIC: https://spti.fi/rZyjX7i 
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- KVRAF
- 25049 posts since 12 Jul, 2003 from West Caprazumia
nope - the chance was 33% before the first door has been opened - there's alway a chance that the car is behind the door that's opened at first - if it is not then there are only two doors left and that's the reason your chances raise - your chance rises the moment the first door is opened and the car is not behind it.Bob Gravy wrote: That can't be right. Think about it. You choose one door out of three so you have a 1/3 chance. You're saying this increases to 1/2 because the host opens a door???
The reason for this is the following:
if you throw a dice there is a 1/6 chance to throw any certain number - if you throw it for the second time and your number hasn't been trown yet your chance is still 1/6. If you throw the dice for the thousandst time and your number hasn't been thrown yet your chance is still 1/6 - but the moment you replace three of the five other numbers by doubling the remaining ones your choice raises to 1/3.
Think about it - the issue with the doors is actually the same situation...
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- KVRAF
- 25049 posts since 12 Jul, 2003 from West Caprazumia
nö - is' bloß das billige Plus-Bier...putte wrote:.. pure magic! ..jens wrote:and so am I ...fabi the underachiever wrote: I am drunk
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- KVRAF
- 1817 posts since 1 Jun, 2003
as said above, i don't know shit, but wouldn't this only count if you took each turn's individual probability? i think if you throw it a thousand times, you have to take into account different probabilities.jens wrote:nope - the chance was 33% before the first door has been opened - there's alway a chance that the car is behind the door that's opened at first - if it is not then there are only two doors left and that's the reason your chances raise - your chance rises the moment the first door is opened and the car is not behind it.Bob Gravy wrote: That can't be right. Think about it. You choose one door out of three so you have a 1/3 chance. You're saying this increases to 1/2 because the host opens a door???
The reason for this is the following:
if you throw a dice there is a 1/6 chance to throw any certain number - if you throw it for the second time and your number hasn't been trown yet your chance is still 1/6. If you throw the dice for the thousandst time and your number hasn't been thrown yet your chance is still 1/6 - but the moment you replace three of the five other numbers by doubling the remaining ones your choice raises to 1/3.
Think about it - the issue with the doors is actually the same situation...
e.g. the probability of a number not turning up, even if you throw the dice a thousand times - now, how likely is that? each turn individually - 1 out of six, but i don't think that holds true for successive rolling...
edit: actually i guess the last part's individual thing wouldn't be one out of six, but five out of six, cause i said NOT turning up, but who's nitpicking, eh?
Last edited by fabi on Sun Oct 23, 2005 11:36 pm, edited 1 time in total.
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- KVRAF
- 25049 posts since 12 Jul, 2003 from West Caprazumia
you could call me as well if you liked to - but as I said I'm drunk... - imagine two drunken kvrians stammering at each other one the phone...fabi the underachiever wrote:
erm, i think i'll call friends in the US now. feel talkative...
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- KVRAF
- 1817 posts since 1 Jun, 2003
i fully agree. but i still don't know... too bad my friend in the US doesn't pick up her phone. probably getting married or something...Bob Gravy wrote:You need to look at the truth table on that link. Your odds stay at 1/3 if you stay put but increase if you move.
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- KVRAF
- 25049 posts since 12 Jul, 2003 from West Caprazumia
fabi the underachiever wrote:I think if you throw it a thousand times, you have to take into account different probabilities.
nope - that's the one counter-intuitive thing about stochastics that's really true:
the probability always stays the same for each new try as long as the conditions (i.e. the number of alternatives) stay the same.
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- KVRAF
- 1817 posts since 1 Jun, 2003
don't know if you meant me, but know perfectly well, what you mean. i wish i had been this perceptive in math class when i was still at school. (and not drunk)Bob Gravy wrote:If you don't believe me try the link to the simulator...
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- KVRAF
- 25049 posts since 12 Jul, 2003 from West Caprazumia
as I cannot look at its code (and even if I could I wouldn't help as I'm not a coder) it doesn't prove a thing!Bob Gravy wrote:If you don't believe me try the link to the simulator...
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- KVRAF
- 1817 posts since 1 Jun, 2003
well, but that is what i mean - it stays the same for each individual try - but does it stay the same when you consider 'has not been rolled the ten previous times' an additional condition? what qualifies as an additional condition?...... hmm. maybe you're right.jens wrote:fabi the underachiever wrote:I think if you throw it a thousand times, you have to take into account different probabilities.
nope - that's the one counter-intuitive thing about stochastics that's really true:
the probability always stays the same for each new try as long as the conditions (i.e. the number of alternatives) stay the same.