Brain teaser

[handsome]

"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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?"

* Behind each of three doors is either a goat or a car (two goats, one car).
* The player picks one of the three doors. The contents are not revealed.
* The game host knows what is behind each door.
* The game host must open one of the remaining doors and must make the offer to switch.
* The game host will always open a door with a goat.
* That is, if the player picks a door with a goat, the game host picks the other door with a goat.
* And if the player picks the door with a car, the game host randomly picks either of the two doors with a goat.
* The host offers the player the chance to either claim what is behind the originally-chosen door, or to switch, claiming what is behind the one remaining door.

Do the player's odds of getting the car increase by switching?

IF YOU HAVE ALREADY HEARD THIS BRAIN TEASER, PLEASE DO NOT PARTICIPATE UNTIL SOME PEOPLE HAVE ATTEMPTED TO ANSWER IT

[2+2 wannabe]

the ol' monty python game

<font color="white">your odds of picking the right one before the "goat" is shown is 1/3 (3 doors to pick from) - after the goat is shown your odds are 1/2 (only 2 doors and one is the prize one is goat). thus, if you switch, your odds are 1/2, and if you don't, your odds are 1/3.</font>

[mmbt0ne]

</font><blockquote><font class="small">En réponse à:</font><hr />
the ol' monty hall game


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[Beerfund]

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IF YOU HAVE ALREADY HEARD THIS BRAIN TEASER, PLEASE DO NOT PARTICIPATE UNTIL SOME PEOPLE HAVE ATTEMPTED TO ANSWER IT

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are you serious? this is posted more than "is internet poker rigged?"

[MagicMan08]

no

[Luzion]

Ive never seen this brain teaser before. But I think it would be beneficial to "switch" your choice.

Lets say for example, there were 1,000 doors; with 999 having goats and one of them having a car. You pick 1 door, and then the game host eliminates 998 of the doors with goats.

Is it beneficial to switch your choice then? I think so. Since the reasoning is that your 1st pick only has 0.1% of getting the right door. The game host eliminating all the wrong choices thus increases your chances greatly to being 50% correct if you switch your choice now.

[Beerfund]

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The game host eliminating all the wrong choices thus increases your chances greatly to being 50%.


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Wrong!

[Luzion]

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The game host eliminating all the wrong choices thus increases your chances greatly to being 50%.


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Wrong!

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Ok, its not 50% since the first door you picked is going to be 99.9% of the time wrong. Should be obvious that switching would be overwhelmingly beneficial right?

[2+2 wannabe]

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the ol' monty hall game


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clearly i'm out of it

[Beerfund]

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The game host eliminating all the wrong choices thus increases your chances greatly to being 50%.


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Wrong!

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Ok, its not 50% since the first door you picked is going to be 99.9% of the time wrong.

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Correct!

[OtisTheMarsupial]

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The game host eliminating all the wrong choices thus increases your chances greatly to being 50%.


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Wrong!

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Ok, its not 50% since the first door you picked is going to be 99.9% of the time wrong.

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Correct!

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More like 66% me thinks.

[MagicMan08]

What the

[imported_anacardo]

I've never understood this.

When Monty reveals the goat, you're essentially being given a new choice, right?

You can switch or "check," and you've got a 50% chance of either being correct.

It seems like you could just close your eyes, take a 20-second walk, come back and choose either door (which is what you're being offered) and your odds would be 1:1.

How can this not be true?

[Luzion]

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The game host eliminating all the wrong choices thus increases your chances greatly to being 50%.


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Wrong!

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Ok, its not 50% since the first door you picked is going to be 99.9% of the time wrong.

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Correct!

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More like 66% me thinks.

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???

I was saying you would be 99.9% wrong in the 1,000 doors example I gave. Yeah, you would be 66% wrong in the 3door example.

[OtisTheMarsupial]

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I was saying you would be 99.9% wrong in the 1,000 doors example I gave. Yeah, you would be 66% wrong in the 3door example.

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Yeah, you're right. I read too fast.
But here's a question for you, what if I want a goat? I like goats. /images/graemlins/smile.gif
Why is this stupid thread in OOT anyway? It belongs in probability. Unless, we're talking about goats, that is.
Goats are gentle creatures that make great cheese. I would very much like to have a goat some day. Does it take a lot of work to care for a goat? Do I need to trim their hooves? Can they live closely with other animals, say a fish? How much do they eat? Can I keep a goat in a city?

[PorscheNGuns]

The 1/3 chance you took when you picked the original door "sticks" to that door, it remains a 1/3 chance.

-Matt

[milliondollaz]

must be the first day of school.

i heard this exact example w/ goats and cars my first day of prob/stat. i also heard the 1000 goat explaination.

isn't that CRAZY how we should switch! anyway, i'm off to buy a lotto ticket

[kyro]

Whoa this is a deep one. I think we should PM BruceZ to help us out. I'm sure he doesn't mind answering the same question 100 times.

[Slow Play Ray]

try it (http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html)

[OtisTheMarsupial]

Can we please start talking about goats now?