Simple IQ Test 3

[Endzone]

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?

[noisyturtle]

Yes, although I would be happy with a goat as well.

[funkymeeba]

Drunken meeba says no.

[damorgue]

Yes, you now have a 50% chance as opposed to the initial 33%. I'll redeem myself from the first one.

[Endzone]

You have a 1 in 3 chance of winning the car if you don't switch doors.  You have a 2 in 3 chance of winning if you switch doors.  It's hard to follow, but this video helps explain it:

http://www.youtube.com/watch?feature=player_embedded&v=mhlc7peGlGg

[SpAmRaY]

I realize this is off topic but couldn't there have been one post for some 'IQ Tests and Other Hard Questions', instead of having a separate thread every single time?

Sorry I'm an old grumpy person

[TheSoulhunter]

Uhm, it's a 1/3 chance initially, but it's 1/2 with 2 doors left no matter if you switch or not...
Door 1 -vs- Door 2 -vs- Door 3 (1/3) -> Door 1 -vs- Door 2 (1/2)
Chance for winning raised as soon one door was eliminated,
it doesn't change by switching from 1 -> 2 eh?

[emptythecache]

a) The "switching increases your chances from 33% to 50%" answer will never make sense to me. The fact that he opens one door, and then asks you again, increases your probabilty to 50% whether you swap or not. Probably is not affected by things that have already happened. Take the coin flipping scenario: The Probably of flipping 4 heads in a row is 1/16, but the probability for each flip is still 1/2. If you flip three heads in a row, the probability that the next one will be heads isn't 1/16 based on your original probability, it's 1/2. So in the Goat/car scenario, he's just changed the scenario. There are two unknown doors, one with a goat, one with a car. You don't have to switch to get the 50% probability, you get it as a virtue of the host changing the odds, period.
b) This question is in the movie 21, as an MIT statistics question, and the fact the "answer" seems patently wrong to me makes me wonder whether I'm stupid, or the movie is.

edit: yes, what thesoulhunter said.

here's the explanation that makes sense to me, from wikipedia: If you adopt the "always switch" policy, the only circumstance during which you will not win the car is if you picked it originally, which was a 33% chance.

[TheSoulhunter]

Looking from the future in the past gives another fun twist to the problem... Chance is determined by the amount of information you have about the process/system. For example, when flipping a dime and having no relevant information about the process/system, chances for either outcome are 50%. But, if you had a huge amount of information (force the coin is flipped with, dimensions and mass of the coin, force vectors, wind conditions, whatever) it would be possible to predict the outcome with only a certain amount of error (unknown factors) left -> Better than 50/50 prediction. Now, by viewing from the starting point at the 3 door scenario (no information), the initial chance that the door you picked was right is 1/3, but viewing from the point where one door is already open back to the starting point (additional information), your chance was 1/2 already after you made your first pick (just that you didn't know about it back then). o.O

Reminds me something I wrote down long time ago:
"Zufall ist nur eine Umschreibung für Geschehnisse die wir aufgrund von fehlenden Informationen nicht mit Sicherheit vorhersagen können"
Translation: "Chance is just a description for the outcome of events we can't predict assuredly because we lack relevant information"

[Halvar]

Reminds me something I wrote down long time ago:
"Zufall ist nur eine Umschreibung für Geschehnisse die wir aufgrund von fehlenden Informationen nicht mit Sicherheit vorhersagen können"
Translation: "Chance is just a description for the outcome of events we can't predict assuredly because we lack relevant information"

Yes, this was considered true in physics until about 100 years ago. 

[TheSoulhunter]

Reminds me something I wrote down long time ago:
"Zufall ist nur eine Umschreibung für Geschehnisse die wir aufgrund von fehlenden Informationen nicht mit Sicherheit vorhersagen können"
Translation: "Chance is just a description for the outcome of events we can't predict assuredly because we lack relevant information"

Yes, this was considered true in physics until about 100 years ago. 

Well, my cat died long time ago and I never played dice... :3
But, can we know that things we predict to be unpredictable couldn't be predicted if had access to information we don't have now?
It's a paradoxon in itself and we kinda step in philosophical matters here, but that's the most fun part about all this, isn't it?

[TheSoulhunter]

In addition, another quote from me: "Everything is predictable but the outcome is unforeseeable"

If I let some object, lets say a spoon, fall (from my hand -> my floor) you can predict that the spoon will most probably hit the floor.
But of course there is still a very small chance that, for example, a bird dives down, grabs the spoon in mid-air and flies away...
Or a wormhole appears for just a split second and absorbs the spoon...

To sum it up:
Check your room for birds and watch the wormhole-forecast to raise your chance for a correct spoon-fall prediction!

[Jagriff]

Yes it's to your advantage to switch. It's very intuitive if you think of the situation with one million doors and the host revealing 999,998 goats upon you picking a door.

[TheSoulhunter]

Yes it's to your advantage to switch.

How is it a advantage when the car is behind door #1 which means switching will make you get the remaining goat?
You can assume it's behind door #2, but the chances for that are as good as for door #1 (one car, two doors)

[keymaster]

There's two "right" answers here.

#1: Yes, because the game show host knows where the goats are and wants to make you lose.
#2: No, because you have a 50/50 shot.

[TheSoulhunter]

There's two "right" answers here.

#1: Yes, because the game show host knows where the goats are and wants to make you lose.
#2: No, because you have a 50/50 shot.

#1: Yes, because the game show host knows where the goats are and wants to make you win as the audience likes to see people win and the show wants high ratings
-> He offers the switch (giving you the possibility for a win as the car is behind the other door)
#2: No, because the game show host knows where the goats are and wants to make you lose
-> He offers the switch (giving you the possibility to loose as it's not behind the other door)
#3: No, because you have a 50/50 shot
-> Without having knowledge about the moderators intentions (usually the case)

:>

Note that you have also a 50/50 chance regarding the moderators intention,
which summed up leaves you again with a 50/50 overall chance...

[E TwentyNine]

You have a 33 1/3 % chance of picking the car the first time.

The key to this type of puzzle is the inclusion of the statement "the host will always open a door to reveal a goat" (which wasn't stated above).  Given that, there's only one right answer.  You should always switch.