Which ones (if any) of these sentences are true?

[RogerS]

And then there's the Two Door problem. Two doors - one is death, the other means life and two people - one outside each door. One person always tells the truth and the other always lies. You are allowed one question to only one of the two.

 

[Kalimna]

For the idots out there (me!) what is the Monty Hall puzzle? And what is Xenos' paradox?

Oh, and from previous page, regarding friction. You don't need friction to move, just ask anyone who observes motion through a vacuum (or as damned close to a vacuum as to render friction zero). What you need is a force that overcomes another force, be it friction, gravity, momentum etc (and I realise Im not using the term 'force' in it's strictest scinetific definition).

Adam S

 

[PeterBassett]

The Monty Hall Puzzle. No peeking, it's all over the internet.

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 No. 1, and the host, who knows what's behind the doors, opens one of the doors with a goat, say No. 3. He will always open a loosing door after you have initially chosen.

He then says to you, "Do you want to pick door No. 2?"

Is it to your advantage to switch your choice?

Do you get better, worse or the same odds of winning if you change the door you picked to No. 2?

 

[Kalimna]

Ahh, I think I know this one - it was (or at least a version) in part of a maths/sciece documentary series (Marcus de Sautoy I think was presenting, and for my money much better at it than Brian Cox who has far too many NigellaLawsonesque floaty camera moves..... but i digress).

I can't remember the logic, but I think it is to your advantage to change your mind.

Adam

 

[PeterBassett]

I think Marcus de Sautoy did a program with Alan Davies and they covered it.

 

[MikeH]

Ah Roger, I sort of remember the life and death doors one. You ask either person which door the other person would say if you asked them which door leads to death and then take that door.
If you had asked the truth giver they would have said that the lier would say the life door.
If you had asked the lier they would tell you that the truth person would tell you the other door.
Or it's something like that anyway!

 

[Jacob]

Just back from the boozer so may get this right!
Your first choice is 1:3 against winning the car. After one goat is eliminated the chances of the remaining choice being a car is 1:2. So you change your choice, 1:2 is better than 1:3.

 

[big soft moose]

Just back from the boozer so may get this right!
Your first choice is 1:3 against winning the car. After one goat is eliminated the chances of the remaining choice being a car is 1:2. So you change your choice, 1:2 is better than 1:3.

initial reasoning is right but answer is wrong - once one goat is eliminated you have a !:2 chance of winning the car regardless of whether you change your choice or not (ie there are two doors left and its 50/50 which has the car)

so there is no advantage to changing your choice, but equally no disadvantage either.

 

[SBJ]

Sorry BSM you are wrong.

you have a 1 in 3 chance of picking the car initially and a 2 in 3 chance of not picking it.
If you get it right initially and change you lose 1 in 3 times.

If you get it wrong initially ( which you will do 2 in 3 attempts, statistically) and then change you will win because the presenter has to remove the second goat.

So in theory, you are better off by selecting the wrong option first time - not that you'd know.

 

[big soft moose]

ahhh pineapples - you are right , and i was wrong - the logic still seems counter inituitive as at the point of choosing its 1/2 as the 3rd option has been removed - but all the sites i googled agree with your interpretation so fairplay

 

[Kalimna]

BSM - Unfortunately for your case I think SBJ is right, and Wikipedia (the source of all fact in the universe!) backs this up :

"An even simpler solution is to reason that switching loses if and only if the player initially picks the car, which happens with probability 1/3, so switching must win with probability 2/3"

There is a lot more explanation in the whole article, but the above line sums it up neatly.

The above can be shown to be the case by experiment, and the initially intuitive answer is, indeed, false. I'm not very good at statistics, and had trouble believing the answer, but the experimental evidence is impossible to refute.

Adam

 

[SBJ]

ahhh pineapples - you are right , and i was wrong - the logic still seems counter inituitive as at the point of choosing its 1/2 as the 3rd option has been removed - but all the sites i googled agree with your interpretation so fairplay

Talk about timing, every time I went to quote you your post changed!!!

What you have to consider is that the presenter introduces an element of knowledge AFTER the intiial choice which you can use to influence your decision.

 

[big soft moose]

ahhh pineapples - you are right , and i was wrong - the logic still seems counter inituitive as at the point of choosing its 1/2 as the 3rd option has been removed - but all the sites i googled agree with your interpretation so fairplay

Talk about timing, every time I went to quote you your post changed!!!

What you have to consider is that the presenter introduces an element of knowledge AFTER the intiial choice which you can use to influence your decision.

the real question tho is what sort of goat and what sort of car - if its a smart car you might be better of with the goat :lol:

 

[bugbear]

The above can be shown to be the case by experiment, and the initially intuitive answer is, indeed, false. I'm not very good at statistics, and had trouble believing the answer, but the experimental evidence is impossible to refute.

Adam

So the "take home" for today: "Common sense answers can be wrong".

Indeed, most good logic or maths puzzles derive much of their appeal from this.

BugBear

 

[Anonymous]

Their experiment wasn't exactly scientific was it

 

[Kalimna]

Mark - yes it was scientific, though not quite as rigorous, perhaps, as the mathematical proof of Fermats Last Theorem. The sample size wasn't huge (50, I think), but the trend was clear and for a tv documentary, I can't think of any way it may have been improved given the time and audience constraints (de Sautoys' docu). Plus, that wasn't the only experimental evidence.

Bugbear - yep, common sense isn't always correct, especially where evidence is counter to what we already 'know'. Just look at any studies involving memory and recall.


Adam

 

[Jacob]

Er - surely common sense does provide the answer?
Clearly the first choice has odds against being the car; is more likely to be goat. The second choice (after removing a goat) has even odds, equal likelihood and so is the better bet.
S'obvious!

 

[PeterBassett]

Its better than 1:2. The odds if your change your mind are 2:3. The odds if you stick with your door are 1:3.

 

[Anonymous]

Well I have just emailed Stephen Hawking the question through the official channels regarding this plane thing.

I very much doubt he will reply as its probably just trivial to him, but thought it was worth a try.

Mstance hasn't changed on it, the plane remains firmly on the conveyor belt. Untill someone who is qualified to challenge my opinion it remains at that.

The Mythbusters experiment wasn't conducted to the true letter of the question so is therefore inconclusive.

 

[Jacob]

Its better than 1:2. The odds if your change your mind are 2:3. The odds if you stick with your door are 1:3.

No. The odds are evens on the change of mind. Still better than 1:3 though.