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# If you can figure this out, you are in the decided minority.

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1. Re: If you can figure this out, you are in the decided minority.
Either that or you've read a book in your time - this is a well known problem that was featured in The Curious Incident of the Dog in the Night-time among others. Though obviously the maths works I have literally never understood it until cambio wechsel's post just there so thank you.
2. Re: If you can figure this out, you are in the decided minority.
(Original post by Arekkusu)
Either that or you've read a book in your time - this is a well known problem that was featured in The Curious Incident of the Dog in the Night-time among others. Though obviously the maths works I have literally never understood it until cambio wechsel's post just there so thank you.
That seems to be the second most common response; the first being 'it's of course 50/50, or 1/2 that you get the car'. People understand it, but just can't get their head around it.
3. Re: If you can figure this out, you are in the decided minority.
(Original post by philistine)
That's the one. Monty Hall? Monty Hall?!
Yes, Monty Hall, not to be confused with Monty Python
4. Re: If you can figure this out, you are in the decided minority.
Seen it before... It's called the monty hall problem, there's a page on wikipeeeja if you want to check your working.
Fwiw prefering goats to cars isn't an option afaict cos they didn't actually let you keep it. Maybe tv trained goats have more value to the company than cars?
5. Re: If you can figure this out, you are in the decided minority.
(Original post by philistine)
(Original post by In One Ear)
I think you didn't define the situation accurately enough, i'll assume that you meant the host deliberately picks the door that doesn't have the car behind it.
Also one must assume that the game show has a standardised format. It must be predefined that the player will pick a door, then the host will open a false door and then an offer to switch will be made. If this isn't defined before the game begins, then probability no longer has a bearing (because the host knows which door is a winner).

But yes this problem is quite simple really, if you give it some thought.

If you pick the right option first time around, then you will definitely lose by switching as the remaining boxes are goat + goat which leaves a goat once the host removes a goat.

If you pick the wrong option first time around, the you will definitely win by switching as the remaining boxes are goat + car which leaves a car once the host removes a goat.

So, switching = winning, if you are wrong the first time around. As there are 3 boxes and it's random chance, you should theoretically be wrong two thirds of the time. So two thirds of the time you win by switching.
6. Re: If you can figure this out, you are in the decided minority.
(Original post by cambio wechsel)
It becomes much easier to understand if you imagine 100 doors. The host has opened 98 to reveal 98 goats. Are you going to stick with your original choice or switch to the other one he has left unopened?
Just thought I'd try to confuse the people who you made this clear to.

If after picking one box out of the hundred he opened one goat door and left ninety eight unopened. You still switch to a new box.
7. Re: If you can figure this out, you are in the decided minority.
Because when you picked your door, you had a 1 in three chance of it being right, so it's likely you were wrong. A definate wrong door has been removed, so the chances are that the other door you're now being offered is right, so that's why you should swap to it.
8. Re: If you can figure this out, you are in the decided minority.
No because behind door number 2 is another goat. Door number one has the car, and that's why the host opened number 3 when you said one.
9. Re: If you can figure this out, you are in the decided minority.
(Original post by philistine)
Try this one out, and be sure to explain your answer because that is the only way it matters:

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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Why or why not?

They say only 5% of the population will come to the correct reasoning of this problem. Can you?
Id say it isn't. You previous choices don't effect what your current chances are.

You started off with a 1 in 3 chance of winning.
Host opens a door, that has a goat behind it
You now have 2 doors, one with a car behind it so you have a 1 in 2 chance of winning
You don't know what door its behind, the host might, but you don't know what the host is thinking. The host could be bluffing or double bluffing. The car may be behind door number 1, and he knows that, so he tried to sway you away to door 2. However, he could also anticipate that you'll think this, so will double bluff and pretend to want you to go to door 2, which is in the fact the door the car is behind.

Until you know what the host is thinking, you can never know. If the question allows a question to be put forward to the host, then thats a whole different scenario, but you can't, so its purely down the chance.

You're making two separate choices and combining the probability that both these will be positive results.

You have a 1 out of 2 chance of winning if you pick either door, and the host removes a goat.

The wiki page demonstrates a table:

However, this demonstrates two different possible scenarios. If you pick door 1, and the host opens door 3, then the first scenario is that, the car could be behind the door that the host opens, which means there would be no point in switching, you would have a 100% chance of being wrong, so that scenario should be eliminated from the table (if the host always picks a goat door then how can this happen?). The table now presents a 1/2 chance of winning.

The second scenario is that the host doesn't pick at random, but instead always picks a goat door, and you pick a random door. Now, initially you have a 1/3 chance and pick a random door. If you're correct, great you've won a car but before you find out the host deliberately opens a goat door eliminating one of the chances. There are only two doors to choose from, so how could your chances possibly be 1/3 ?

I really don't understand how people are getting 2/3. I don't know if i'm missing something or this is some quantum **** going on but this is annoying me far too much.
Last edited by Gwalchgwyn; 15-04-2012 at 19:32.
10. Re: If you can figure this out, you are in the decided minority.
Yes, you do want to switch. The only way you will lose by switching is if you were already on the door with a car, a 1 in 3 chance, because you'll switch to a door with a goat. If you were on either door with a goat and now know where the other goat is located, by switching you'll go to the car. You have greater chance of choosing a door with a goat, indeed a 2 in 3 chance.

In short, switching means you leave with a car two out of three times.
11. Re: If you can figure this out, you are in the decided minority.
I think most people on this site has heard of the Monty Hall problem, tbh.

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Last updated: April 15, 2012
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