Of cabbages and cars
You are the contestant on a game show.
The host shows you 3 doors.
Behind two of the doors is a cabbage. Behind one of them is a car.
The host asks you to select a door.
The host opens a DIFFERENT door to the one you chose, revealing a cabbage.
The host asks you if you want to pick a different door, or stick with the one you have.

Presuming you want a car, should you change or stick?
(CADmonkey rollllllllled another one, just like the other one, Sat 15 Oct 2011, 18:24, 17 replies)

Change.
You have a two in three chance of getting the car. If you don't change you have a 1 in 3 chance.
(dchurch bah, Sat 15 Oct 2011, 18:49, closed)

Please show your working.
This brings back dim memories of Marylin vos Savant explaining the maths behind this on a TV show once, but since she has an IQ of 228 and I was about 7 (years old) at the time, my memory needs refreshing.
( .Yeti., Sat 15 Oct 2011, 18:52, closed)

This is the usual reasoning:
You have a 2 in 3 chance of having picked a door with a cabbage. If this is so, then there's one door with a cabbage and one with a car left. Given that the host has shown you one with a cabbage, the other one will have the car.

You have a 1 in 3 chance of having picked the door with the car. If this is so, then you'll get a cabbage by changing.

Changing gives you a 2/3 chance of getting the car, and staying gives you a 1/3 chance. Thus you should change.

---

But actually it depends why the host picked a door with a cabbage behind it (ie do they know where the car is, and do they want you to win or lose). See en.wikipedia.org/wiki/Monty_Hall_problem
(apeloverage committed the vile act of onanism on, Sat 15 Oct 2011, 19:30, closed)

Easy.
The first door you pick has a one-third chance of having a car behind it. The two remaining doors therefore have a two-thirds chance of having a car behind one of them.

If you could choose both of those doors, I'm sure you'd agree you'd have a two-thirds chance of getting the car - but you don't have to! The host, who knows where the cabbages are, removes one of those two doors from play - meaning the door that neither yourself or the host chose has the car behind it two-thirds of the time.

If the host didn't know where the cabbages were, the odds would be equal, but he'd sometimes open the door with the car behind it.
( Legionary - My god, Brian, there's a message in my alphabets, Sun 16 Oct 2011, 12:03, closed)

But...
Suppose you choose door 1
The host opens door 2
You swap to door 3.

Now the host asks "are you sure?"

Now you have the choice between door 3, or doors 1&2

By the logic of the 'correct' answer, you should always swap and keep swapping. This can't be right, can it?
( Ghoti Fingers, Sun 16 Oct 2011, 16:44, closed)

No, it's not :)
The odds of your first choice being right are always one third, because you made that choice when there were three doors. That doesn't change when the host opens one of the two other doors - and so you should always switch (once), because you can either stick with your original choice (with a one-third chance of being correct) or switch to the only remaining door.

Remember, the key is that the host knows where the car is, so he never opens that door. Without that knowledge, it wouldn't make any difference whether or not you switched, but one third of the time the host would accidentally open the door with the car behind it. His simply asking "Are you sure?" without opening a door doesn't make any difference.
( Legionary - My god, Brian, there's a message in my alphabets, Sun 16 Oct 2011, 18:59, closed)

Tell the host to open the right fucking door for starters then punch him in the face and steal 20 quid off him.

( Amorous Badger NAKED BEA ARTHUR PHOTOS 4U, Sat 15 Oct 2011, 19:00, closed)

RthoughsomecatshitwhilstOFL
Oh Mr.Badger you are SUCH a wag. I simply didn't see that one coming!And from your good self, of all people. Pray, hit me with another!
(CADmonkey rollllllllled another one, just like the other one, Sat 15 Oct 2011, 19:18, closed)

Oh man, I'll totally be able to claim another 20 quid if I do that.

( Amorous Badger NAKED BEA ARTHUR PHOTOS 4U, Sat 15 Oct 2011, 20:12, closed)

what she said

(CactusZack Shaved his coin purse on, Sat 15 Oct 2011, 20:05, closed)

Cabbage
Bio-organic matter than can be seeded and replicated to feed and encourage future workers to build cars that can be further used to distribute valuable cabbage seedlings.

Plus you got more of a chance to get a cabbage. You'd be foolish not to.

*May be scientifically fabricated. /knows nothing about cabbages or cars.
(mr-lizard Hell's teeth man!, Sat 15 Oct 2011, 19:42, closed)

You change.
But this only works if the game show host knows which one has the cabbage.

~~~~~~~~~~~~~~~~ lots of maths ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You need to change
( Mrs Entity is in hiding., Sat 15 Oct 2011, 20:03, closed)

My logic
is if one door has already been opened to reveal a cabbage, there are two doors left. One has a cabbage and one a car, so you have an even chance of having chosen the car or the other cabbage already. This also gives you an even chance of getting the car whether you change or stick, take your pick.
(Classic Ray, Sun 16 Oct 2011, 4:02, closed)

Bzzzt Error!
Thank you for playing.
Didn't he do well ladies and gents...

After the break we'll be talking to a welder from Birmingham who's going to explain the theory of time travel after having had a "really good idea" whilst in the Dog and Ferret.
( DukeEuphoria Comes highly reccomended, Mon 17 Oct 2011, 14:56, closed)

Taking into account the fact that the presenter opened a different door
there are two different scenarios.

1. The presenter opened a different door because you chose correctly and he's trying to throw you off, in which case there is a 100% probability that your original choice was correct.

2. The presenter didn't care which door you chose originally and is just trying to screw with your head and/or pad out the show, in which case there is a 50% probability that your original choice was correct.

Combining the two (and this is where my memory of probability math fails me - but it was nearly 30 years ago), there is then a 75% chance that your original choice was correct, so you should stick by it.
( argyleblanket The man on the roof works for me, Sun 16 Oct 2011, 9:36, closed)

But since the host always opens a door
...what his motivation is doesn't matter. And I'd argue with that 50% figure as well - see my reasoning above :)

(This is an example of the Monty Hall problem, by the way.)
( Legionary - My god, Brian, there's a message in my alphabets, Sun 16 Oct 2011, 12:18, closed)

If you are a contestant on a game show,
go and have your head examined.
(bat_fudgie, Mon 17 Oct 2011, 21:54, closed)