Cars and goats....

Forum Moderator Joined: 18 Feb 2004 Posts: 7432

Say youâ€™re on a game show that has a wall with three doors. Behind two of the doors are goats, and behind the other is a shiny new 19 16v (or a clio for roger). You are asked to pick a door, and will win whatever is behind it. Obviously you donâ€™t know what is behind which door. Before the door you pick is opened, however, the show host, who knows what's behind the doors, opens one of the other two doors to reveal a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened).

So to break it down:

Â· Behind each of the three doors is either a goat or a car (two goats, one car)
Â· You pick one of the three doors. The contents are not revealed
Â· The game host knows what is behind each door
Â· The game host must open one of the remaining doors and must make the offer to change your choice
Â· The game host will always open a door with a goat

Do your odds of getting the car increase by changing your choice of door?

Forum Moderator Joined: 02 Mar 2004 Posts: 19978

if its out of the top and bottom door and ther eprizes are behind them then the lower door will be the wise choice.

assuming a pyramid formation.

Forum Moderator Joined: 18 Feb 2004 Posts: 7432

theyre side by side doors Chris Rolling Eyes

Forum Moderator Joined: 02 Mar 2004 Posts: 19978

arse. Must only be dodgy scottish ones that have them on different levels!

So no by choosing the other door will not increase your chances as its 50/50

Mr Quoter-vator Joined: 16 Feb 2004 Posts: 7405

ive seen this in another context. Cannot remember the explanation.

Just thinking about it, when you first pick a door you have a 33.33% chance of being right.

If he then shows you one goat and says you can change your mind, do you now have a 50% chance of being right as you know the car is behind one of two doors.

or was it that somehow it looks like your chances have gone up but somehow they haven't?

Level 8 User Joined: 14 Apr 2004 Posts: 278

Changing the choice of door makes no odds to your odds as the two unknowns remain. However as JB said, the host revealing one of the goats does.

The garage style 'up and over' door will be the one to go for...

Forum Moderator Joined: 18 Feb 2004 Posts: 7432

The answer is, it is in your advantage to change doors.

66% of the time you will win the car by switching doors after the goat has been revealed

Level 8 User Joined: 14 Apr 2004 Posts: 278

Is there a logical reason why there is an advantage? or is it Murphy's Law?

Forum Moderator Joined: 18 Feb 2004 Posts: 7432

Itâ€™s a quantum mechanics problem. Yes, there is a logical reason, although it is counter-intuitive.

Lets look at it another way with bigger numbers.

I shuffle a deck of cards and get you to pick one at random and put it on the table in front of you without looking at it.

What is the probability that you picked the ace of spades?

1/52, right?

And what is the probability that I still have the ace of spades in my hand?

51/52, yes?

Now, I put down 50 of the 51 cards I have in my hand. If I have the ace of spades, I keep it and put allthe others down. If I donâ€™t have it, I just randomly pick one of my cards and put the other 50 down.

What now is the probability that you picked the ace of spades?

STILL 1/52

And the probability that I had the ace of spades?

STILL 51/52

Therefore if I give you the option to swap cards with me, 51/52 times, you will get the ace of spades by swapping.

Mr Quoter-vator Joined: 16 Feb 2004 Posts: 7405

Forum Moderator Joined: 18 Feb 2004 Posts: 7432

Guess whos been given a clipart CD recently.... Laughing

Mr Quoter-vator Joined: 16 Feb 2004 Posts: 7405

i got it off the web Very Happy

Site Subscriber Joined: 13 Oct 2004 Posts: 4722

who cares?

get a car if you win

get a goat if you loose

its win win for schackal.

Mr Quoter-vator Joined: 16 Feb 2004 Posts: 7405

ooooooo

Forum Moderator Joined: 18 Feb 2004 Posts: 7432

heheh....

Mr Quoter-vator Joined: 16 Feb 2004 Posts: 7405

Roger and Schaks in Scotland.... Laughing

intepret as you like.

Site Subscriber Joined: 11 Feb 2005 Posts: 2929