Try this one on your mates... it's always a good one for an argument :) (Even after you've attempted to explain the answer)

Suppose you're on a game show, and you're given the choice of three doors:
Behind one door is a car; behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He then says to you, ``Do you want to pick door number 2?''

Is it to your advantage to switch your choice?

Does it matter if you change your mind?

No, you're left with a 50/50 chance of getting a goat or the car.

but what if you prefered the goat to the car?

When you made your first choice you had a 1 in 3 chance of picking the right door but now you would have a 1 in 2 chance which is a big improvement. So, with your initial choice your are more than likely to have been wrong, by swapping you are just as likely to make the right choice as the wrong one. Using that logic, I'd say swap.

But, statistics and chance don't mix so it doesn't really matter, you're going to get the goat whatever.

Originally posted by tinajones
but what if you prefered the goat to the car?

:o :o :o

c'mon think about it! pet goat with free goats cheese.

Originally posted by tinajones
c'mon think about it! pet goat with free goats cheese.

Oh right.
Sorry.
My mind is obviously deprived.
I thought....erm.... no lets not go there.

Anyway, the question still stands (if you want the goat or not) - does it make a difference if you change doors?

Nomme

oh god no! you thought i wanted to get all goated-up! gross all that beastyality stuff. just an innocent pet is what i'm on about. mind you loadsa people talk about cars in a sexual way so i'll let you off .

Originally posted by tinajones
oh god no! you thought i wanted to get all goated-up! gross all that beastyality stuff. just an innocent pet is what i'm on about.

:blush: :blush: :blush:

oooh I am so confused now.

Originally posted by Lindseyw
oooh I am so confused now.
How do you confuse an idiot?


Purple!

mmm.... I have come across this problem before, see

URL Removed

I knew the problem and gave an answer, why do I need to type hundred of word in explaining the solution when I found a website to do it for me?

Mmm... it a case of, don't answer it if you know... if you do not know then have a go.

Originally posted by John
mmm.... I have come across this problem before, see
[snip]



Booooo!

You could have let people who've not heard of it before have a go before posting the answer. The thing the gets me about this problem is that even when they are told the answer they still refuse to believe it.

Nomme

It's similar but not the same. The one behind the link does not say what's behind the door the host opens.

Still plenty of room for debate and confusion.

Reminds me of the scam about having 11 fingers

which I do.........

Dont believe me?

Simple, just watch, starting with the little finger on my left hand I will count down from 10, the little finger being 10, my ring finger 9, my middle finger 8, my index finger 7 and my thumb 6, and there are five fingers on the other hand makes 11 - right?

Try it yourself

I so blue

Originally posted by nommedenet
Booooo!

You could have let people who've not heard of it before have a go before posting the answer. The thing the gets me about this problem is that even when they are told the answer they still refuse to believe it.

Nomme
Yeah ,it's counter intuitive. But you should really change your mind. Note. this only works if you do it hundreds of times over.

There's a whole heap of this stuff in Metamagical Themas by Doug Hofstadter, and the many and varied books by Martin Gardner.

Anyone ever heard of the luring lottery?

Now nomme as my partner, i have had enough of the goat thing. Stop it now. This is all Sebs fault and will have to stop u goin out with him

Originally posted by fuzzy purple
Now nomme as my partner, i have had enough of the goat thing. Stop it now. This is all Sebs fault and will have to stop u goin out with him
HAHA Nomme got a telling off!

well it really makes no difference bcos if you asked for 1 and he opened 3 that means (knowing most game shows) that the car IS behind 1 so even if you do pick 2 your still going to get a goat so it makes no difference

cum on people i would of thought that some one would of got that already

and im a young un too

Fletch

Originally posted by Fletch
well it really makes no difference bcos if you asked for 1 and he opened 3 that means (knowing most game shows) that the car IS behind 1 so even if you do pick 2 your still going to get a goat so it makes no difference

cum on people i would of thought that some one would of got that already

and im a young un too

Fletch

Ah Grasshopper you have much to learn....

...like the fact that when you post here your messages are time stamped.

So explain to me how you time to read and post the above (when you should have been in bed!) but somehow didn't have time to do the washing up?

Eh? Eh?

In fact it does make a difference and you should change doors to increase your chances of winning.

You are wronger than Mr. Wrong from Error Town, Mistakeville, having a bad day.

If you don't believe me try googling for the following : 'Monte Hall Problem'

Nomme

>>In fact it does make a difference and you should change doors to increase your chances of winning. <<

Er... i think not.
It makes no difference at all.

There is NO increased chance if you change you door.

Its not that hard to work out, :?!

If you toss a coin 5 times and the first four times are tails, its not more likely that the fith toss will give a head! (Not the same logic as the door thing, but still)

Originally posted by Jethro
>>In fact it does make a difference and you should change doors to increase your chances of winning. <<

Er... i think not.
It makes no difference at all.

There is NO increased chance if you change you door.

Its not that hard to work out, :?!

If you toss a coin 5 times and the first four times are tails, its not more likely that the fith toss will give a head! (Not the same logic as the door thing, but still)

Like I said earlier, people still refuse to believe that it makes a difference even after its been explained to them.

Did you do that google search I suggested Jethro? Do it. Google for 'Monte Hall Problem'. A lot of people have given this a lot of thought - certainly more than the 30 seconds you probably thought about it.

One result from such search is this page : http://www.cut-the-knot.org/hall.shtml

It has an explanation and a simulation so you could try it for yourself.

regards
Nomme

The best way to think about it is to say to yourself, which door isn't it in and pick it but choose the other when offered.

Your chances are increased because basically you are choosing 2 doors instead of one if you think of it that way.

Nope, im sorry you are wrong.

There is no change in probibility from the start.

Lets think though this...

There are three doors - you pick one at random.

The chance if picking each door is 1/3 - ok?

Door1 - 1/3
Door2 - 1/3
Door3 - 1/3

Right, now, one is opened - this one DOES NOT contain the prize, ok - that right?

The door opened will be one of the doors you didnt choose.

Right, lets underline the above, and look at the next stage...

Regardless of any previous choices, you have two doors to pick from (lets forget which one you first chose).

Behind one door is the prize, behind the other is not.

You can shoose either - at random (so in effect deciding to 'stay' or 'change' doors).

The change now of picking the correct door is 1/2, ok?

Because this 1/2 probibility is not dependant on the previous decision, the probibility is the same.

So, to conclude - WHICHEVER door you pick to start with (1/3) you
are then faced with TWO doors, one without and one with the prize (1/2).

As for the maths site with the javascript - dont beleive everything you read.

Now, although i could be wrong, i am very sure of myself on this.

Any maths students here?

Tim

That would have worked Tim

EXCEPT that the whole point of the exercise is that you do NOT know if the first door has a goat, a car or a naked man behind it, not even after you have initially chosen it....

Okay?


You are still no nearer to knowing, as you conduct this experiment, whether you have already picked the prize


- or else why would you even be asked to consider picking another door, you would either say
1. I like this prize best out of the alternatives so I am not opening any more doors thanks
or
2. I dont fancy this much, give me another chance

That wouldnt take up much of a thread would it now....

Its true...

You had 1 in 3 chance of getting the correct door for the star prize.

The host then choses from the remaining 2 doors.

If you failed in your 1 in 3 (66% chance of failure) attempt to get the star prize - the host is forced to choose the goat in his/her attempt, thrust increasing the probability that the remaining door is more likely to have the car.


Think of it this way... You pick one door.

The host picks the remaining two.

Just before he opens the door to the goat, do you want to stick with what you have choosen 1 door or swap for the other 2 doors?

The maths is a bit more tricky than that its not 66% chance of winning the prize because you have to take into account that you may have indeed choosen the star prize in your lucky attempt.

Do this often enough it shows that it is more favourable to swap.

>>EXCEPT that the whole point of the exercise is that you do NOT know if the first door has a goat, a car or a naked man behind it, not even after you have initially chosen it....<<

I know that! Read what i wrote again.

>>If you failed in your 1 in 3 (66% chance of failure) attempt to get the star prize - the host is forced to choose the goat in his/her attempt, thrust increasing the probability that the remaining door is more likely to have the car.<<

...no, the host is forced to choose the goat REGARDLESS of if you choose the prize door or not! Hence it doesnt make a difference. Only that if you pick the prize the first time, the host has to make a decision - but that is not relevent because you wouldnt know.

Of the two ramaining doors one has the prize behind - this is true regradless of your first decision.

You choose one of three - one of the doors you didnt choose is opened with a goat behind- you choose one of the two remaining doors.
The above applies whether you picked the correct door in the first place or not.

Also, but not relevent to this discussion, the overall probability ends up at 50/50, so from the begining you have a 50/50 chance of winning the car. (Because there is one goat, you cant win - as the host reveals it).


Tim

Let change the format of the show.

You are basically doing the same thing, but the show format is changed slightly different, you still only win 1 prize, but can choose from the two doors remaining.

Choose the door which DOESN'T have the star prize...

You choose door 1.

The host says OK, lets reveal what behind Door 2 and door 3 to see if it has the Star prize.

Lets see what behind door 3 first, surprise, surprise... its a goat.

Shall we see what behind door 2?

In this format, is this sequence of event 50/50?