stephen_gusterson
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| posted on 29/1/04 at 03:31 PM |
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maths question
I read a book yesterday - even tho there was hardly any pictures in it.
It won the whitbread prize and is an excellent read - The Curious Incident of the dog in the night time - by Mark Haddon.
In it is a rather stange maths related question on probabilities.
Its called the monty hall problem.
it goes like this.
you are in a game show. you can win a car as a prize. The game show host tells you there is a car behind one of three doors. The other two doors have
goats behind. You choose a door. He then opens a door which isnt the one you chose. There is a goat there. The host asks if you want to change your
mind.
do you stick, or change to get the best possibility of winning? Or is it the same?
atb
steve
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theconrodkid
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| posted on 29/1/04 at 03:36 PM |
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i,d keep the goat
who cares who wins
pass the pork pies
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ned
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| posted on 29/1/04 at 03:38 PM |
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i'd whack him with a kipper and tell him to open the bloody door i chose.
Ned.
beware, I've got yellow skin
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splitrivet
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| posted on 29/1/04 at 03:46 PM |
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quote:
Originally posted by theconrodkid
i,d keep the goat
So would I,but only if it was a good looking one.
Cheers,
Bob
I used to be a Werewolf but I'm alright nowwoooooooooooooo
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locoboy
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| posted on 29/1/04 at 03:50 PM |
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Stevo did you honestly expect a serious reply!
if the host doesnt change what is behind the doors aftershowing you his goat  you will have 1 in 2 chance of guessing the right door if you opt for
the change your mind option, as opposed to a 1 in 3 chance of getting it right when you innitially choose which door to open.
hope that makes sense!
ATB
Locoboy
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Alan B
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| posted on 29/1/04 at 03:52 PM |
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No point in changing...all it tells you is that you now have a 1 in 2 chance instead of a 1 in 3 when you started...
Seriously though,...the goat..naked or kinky undies on?
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Alan B
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| posted on 29/1/04 at 03:53 PM |
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Damn Col....beat me to it...
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200mph
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| posted on 29/1/04 at 03:57 PM |
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hi.... this is in fact a serious reply to your question.
My girlfriend was studying Economic last year, and she posed me this question, although subtely different.
If I remember correctly, you should always change. this seemed really daft to me at the time, and although I like to think of myself as a smartish
guy, it stumped me for a bit.
Think she tried to explain it like she would to another girl!!
Anyways, will ask her again tonight, and see if i can confirm it.
theres another piece of useless information for anyone who ever enters a chatshow!!
Mark
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splitrivet
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| posted on 29/1/04 at 04:00 PM |
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quote:
Originally posted by Alan B
Seriously though,...the goat..naked or kinky undies on?
Obviously your missus hasnt given you your bromide again today Alan.
Cheers,
Bob
I used to be a Werewolf but I'm alright nowwoooooooooooooo
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GO
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| posted on 29/1/04 at 04:01 PM |
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Col, you're right,supposedly mathematically you've got a better chance if you change your mind but I dont beleive it! Loads of people have
written computer simulations to prove it but I still think its rubbish.
Now, if it was a sheep behind the door it would be awhole nother matter...
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Cussed
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| posted on 29/1/04 at 04:04 PM |
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Always change
As Colmaccol has already said; the answer is you should always change. It's one of the probability questions that always messes with heads.
If you stick with your original guess then you have a 1 in 3 chance of being right, if you change then you have a 1 in 2 chance of winning.
If you think about it too much steam will start to come out of your ears.
The other thing to consider is, do you want a goat or the car?
Other than this, is it a good book? I've been thinking of getting rid of some booktokens on it How would you rate it on the scale from Robin
Hood to Dax?
Eddie
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JoelP
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| posted on 29/1/04 at 06:12 PM |
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wrong
when he opens the door he reduces the odds of you having chosen correctly to 1 in 2. it is 50 50 either way.
all that changes is that one remaining door is a goat, and one is the car. its the same whichever you choose.
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stephen_gusterson
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| posted on 29/1/04 at 06:12 PM |
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you are right - i did forget where I was posting this question ! 
I will post a piccie later on of the correct answer (decision tree) - some of you are close, but not exactly right........ you should change - but
what are the overall odds improved to?
atb
steve
[Edited on 29/1/04 by stephen_gusterson]
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JoelP
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| posted on 29/1/04 at 06:17 PM |
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surely the only way the odds can change is if he opens the door you selected and says goat! do you wanna change?
im gonna have a think since i was sure just now...
edit: heres the crack!
you've picked one, seen a goat in another door, and then you have a choice. there are two doors to choose from, so from here it is 50 50 which
is the car. so if you stay with your original choice, there is a 50% chance you were correct, and if you choose the other, again there is a 50% chance
you will now be right. you cant choose the door he opened, so thats part of the chance gone.
the key is that, if you didnt tell the dude what door you had chosen, he might open the door you chose immediately. then you would have to change. as
such its not random which door he opens. not sure how that affects it but it seems relevant in some way.
it seems pretty insurmountable, almost like a paradox, and paradox's dont exist in my books! at first it is definately 1 in 3, and at the end it
is definately 1 in 2. but changing will make no difference cos its already 1 in 2 whatever you choose.
its like the lottery, when the first 5 balls have been matched its down to 1 in 37 ish, not 1 in 14m, but changing the last ball makes no difference
then...
this reminds me of that ridiculous question about a dinner lady trying to return change to 3 people and the mad sum that results, if you remmeber that
one...
anyways steve, do you have a tree of this? its quite complex due to man opening the door not being random.
[Edited on 29/1/04 by JoelP]
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Alan B
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| posted on 29/1/04 at 06:17 PM |
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Steve and all,
I will take a LOT of convincing that by changing your choice you have improved your chances.....as I see it is still 50:50 either door.
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JoelP
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| posted on 29/1/04 at 06:28 PM |
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damn right alan!! i'd love someone to prove me wrong though cos it is quite baffling.
how come we always seem to agree on stuff though?!?
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Alan B
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| posted on 29/1/04 at 06:36 PM |
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Easy mate...cos' we're f*****g right...
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200mph
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| posted on 29/1/04 at 07:00 PM |
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Ok,
I had this figured out a minute ago, but am all confused now!!
At the start the probability of you being correct is 0.33 (ish), i.e. a 1 in three chance of success (lets say you pick door number 1). That
consequently means that there is a 2/3 chance of being wrong.
So, there is 2/3 chance that the other two doors contain the car(either in door number 2 or number 3).
The guy tells you one of the other doors (number 3 for example) is a goat, which takes it away, meaning there is a 2/3 chance that the remaining door
(number 2) has the car.
Also follows, if in doubt, go for the middle one!!
Mark
[Edited on 29/1/04 by 9904169]
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JoelP
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| posted on 29/1/04 at 07:08 PM |
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quote:
Originally posted by 9904169
The guy tells you one of the other doors (number 3 for example) is a goat, which takes it away, meaning there is a 2/3 chance that the remaining door
(number 2) has the car.
Mark
[Edited on 29/1/04 by 9904169]
it cant be a 2 in 3 chance of it being door two, cos it is actually 1 in 2. one car, two doors. the non random event of him choosing a door to reveal
changes it.
there are two remaining doors, and one goat, and one car. if changing your mind increases your odds, that would imply you were wrong in the
beginning.
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200mph
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| posted on 29/1/04 at 07:16 PM |
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not really.
ok, between doors two and three there is a 66% chance, ok, as its two out of three. All that effectively happens is that as door three is removed,
all of that 66% chance transfers to door two.
Crazy I know, but true.
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200mph
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| posted on 29/1/04 at 07:18 PM |
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should put this in as an edit I know, but tuff.
being wrong from the beginning doesnt come into it, as at the start, with no other information, you have a one in three chance. So of course most of
the time (67%) you will be wrong.
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stephen_gusterson
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| posted on 29/1/04 at 07:55 PM |
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it IS a 2 in 3 chance.
I will let you stew a bit and post the answer later.
apparently when this concept first came out it caused an uproar in the mathematicw world.
but the drawing I will post will prove its 2 in 3
atb
steve
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200mph
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| posted on 29/1/04 at 07:58 PM |
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ouch, have just hurt my arm trying to pat myself on the back
I think it's all about seperating the right odds from the wrong ones
[Edited on 29/1/04 by 9904169]
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ijohnston99
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| posted on 29/1/04 at 08:22 PM |
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The answer is 42.
Simple!
Ian
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Peteff
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| posted on 29/1/04 at 08:38 PM |
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Are these big doors to hide a car behind or small doors to hide a goat behind or is it a small car . Personally I would use Bayes' theorem
depending on which door was opened to lower the odds on you getting the right choice.
P(C|host opens B) = p(C)*p(host opens B|C)/p(host opens B)
= (1/3)/(1/2)
= 2/3
This of course presumes you chose door A and were shown behind door B In which case you should change choice to door C.
yours, Pete.
A=1 B=2 C=3 and P is probability constant
[Edited on 29/1/04 by Peteff]
[Edited on 29/1/04 by Peteff]
yours, Pete
I went into the RSPCA office the other day. It was so small you could hardly swing a cat in there.
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