Settle an argument...

[moa]

You are on a gameshow; A rather boring one where there are three doors to choose from. Two of the doors conceal a goat each while the third conceals a brand new car. You are asked to pick a door. Say you pick door two. The gameshow host then opens door one and reveals a goat. He/she then asks you if you wish to change your mind and pick door three. Assuming you want to win a car you should change your mind right as the odds are in your favour?

[CBrine]

I'm wondering who exactly it is that you are aurguing with that actually wants to keep the goat? And has anyone slapped them on the side of the head recently? If not, please do so for me.

:biglaugh:

[moa]

It's a nubian goat (good milk).:yes

[Zack Barresse]

The odds are neither in your favor nor the gameshows. Even if the gameshow knew what door the second goat was behind, there are only two doors left for you to choose. Since choice is with the contestant, the odds remain the same regardless of where the goat may be placed. Odds remain at 50/50, which leaves a completely even playing field for either choice made by the contestant.

The only other thing one would need to know is any outstanding variables. Can the contestant physically open the doors? Can s/he get to the doors, especially without falling through a trap door? Is this outdoors? Weather? Is the gameshow a reputable show with a devilishly handsome host? Sidehost? Second prizes? Third prizes? Important questions...

[Bob Phillips]

The only other thing one would need to know is any outstanding variables. Can the contestant physically open the doors? Can s/he get to the doors, especially without falling through a trap door? Is this outdoors? Weather? Is the gameshow a reputable show with a devilishly handsome host? Sidehost? Second prizes? Third prizes? Important questions...


... and has Zack lost it?

[Zack Barresse]

Lost what? I'm right here.

[moa]

Yes but you have a 2 in 3 chance of picking a goat at the start. When the door is opened to reveal a goat you are still more likely to have chosen a door with a goat than a car so you should switch.

Does that make sense to anyone else? Can somebody explain it mathematically?

[johnske]

This is called the Monty Hall problem, it's not 50/50 - your chances of winning goes to 66% if you switch. Bayes theorem explains it, read here (http://en.wikipedia.org/wiki/Monty_Hall_problem#Bayes.27_theorem)

[moa]

I found the answer by googling "Two goats and a car".

I clicked I'm feeling lucky...

[CBrine]

So, aftering reading that, it seems the variability occurs because the contestent is just as likely to switch from a winning answer to a losing answer, as they are to switch from a losing answer to a winning answer.

Who'ed thought this much anaylsis would have gone into the Monty Hall show.:-) Mathamatician's have to much time on thier hands.

(No offense to any mathamatician's frequenting this board. Especially Aladin who's help I may need in the future)

[moa]

True enough CBrine although I am glad I now have concrete proof to throw in someone's face.:)

My girlfriend will not be pleased but she's bound to claim that the question was badly phrased...

Time to hit the office Christmas party...:beerchug:

Merry Christmas.

[Bob Phillips]

Who'ed thought this much anaylsis would have gone into the Monty Hall show.:-) Mathamatician's have to much time on thier hands.
Reminds me of the story about the German mathematician David Hilbert. Noticing that one of his students had been absent from class for some days, Hilbert inquired the reason. He was told that the absentee had abandoned his studies in order to become a poet. Hilbert said, “I'm not surprised, I never thought he had enough imagination to be a mathematician.”

Oh, and mathematicians can spell.

[Zack Barresse]

LOL! So, what are you trying to say Bob? :D

[johnske]

The easiest way of looking at this problem is if you imagine a contestant who has 3 cards to choose from, but only one card is the winning card.

The contestant chooses one card and thus has only a 1/3 probability of winning. Monty is left with 2 cards and the probability of one of them being the winning card (and Monty being the winner) is 2/3.

In this game, the main difference between the contestant and Monty is that Monty is allowed to look at his cards and the contestant isn't, so the game is biased.

Now Monty is certainly not going to discard and expose the winning card, so the probability of his having the winning card in his hand is (still) 2/3.

So when Monty asks the contestant if he wants to swap cards with him, he's really asking if the contestant wants to swap Montys original 2/3 probability of having the winning card with the contestants 1/3 probability of having chosen the winning card - the contestants chance of having the winning card is only half the chance that Monty has it, so they'd be a fool if they didn't swap :)

[Bob Phillips]

LOL! So, what are you trying to say Bob? :D

That mathematicians are the highest evolved life form.

[Zack Barresse]

And there it is folks. :yes

[CBrine]

Oh, and mathematicians can spell.
Can't spell without Word, can't add without Excel, too lazy to press the spell check button.

[XLGibbs]

A very popular and oft debated math problem. 66.6% from the start. Since the gameshow host does not reveal what is behind the 1st door, your odds are always better at changing Since you go from 50/50 to 2/3.

[malik641]

There's been a discussion here about it before, with some code from mvidas to display the results of switching or not switching. It was pretty cool.

Check it out here (http://www.vbaexpress.com/forum/showthread.php?t=8538&highlight=door).


And for my 2 cents: always switch the door in the end. You're better off.

[shades]

That mathematicians are the highest evolved life form.
Bob, I knew I liked you!!!

BS in Major: Math/ Minors: Physics/Education (era: while the Vietnam War was at its peak, before desktop computers, before handheld calculators, and I never did know how to use a slide rule - everything was in my head or notes in long-hand!):p

[malik641]

That mathematicians are the highest evolved life form.
http://www.vbaexpress.com/forum/images/icons/icon10.gif