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# The Monty Hall problem

alalex
This is just for fun, since I love how people prove the answers.
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Here is the problem:
There is a TV show, with three shows. Two of them contain goats, the other one a car. A person gets to choose one. Then, the host opens a door containing a goat, obviously he knows where the car is. And the person has to decide whether to switch door, or stick with the door he already got.
Some people say it doesn't matter because it is 50/50% chance. Others say it is better to switch door.

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Make your choice, the best prove gets 50 \$frihs by now. Maybe more if I like the prove.
Hammy
You got a Typo there:

 Quote: There is a TV show, with three shows.

Hmm.. It all depends on what the prize really is lol. Maybe the prize is the goat?.
Perhaps if he's a goat farmer, he'd love to win a goat? Goats ar emuch more productive than cars, you can get milk from them, you can use them as a form as tranport i guess, much cheaper to maintain than cars. Cars are more deadly, expensive to run, and the guy might like protecting the environment and much prefer goats to graze on grass.

Tho, if the end door was open, he should change to the other end door, cuz it's ovious the goats would be together lol.. cuz thats where i'd put them .

Can the guy drive?

Anyway, the car is behind door number 2 so there :p lol
It should be a speedboat!! lol :p

Hammy.
mathiaus
Well theres a 50/50 chance of the car or another goat. hes already got a goat so he wont loose anything by gambling but he could win more so gamble.
ninjakannon
There is a higher chance that you will initially choose a box with a goat in (66%). On choosing a box with a goat in, the host will have to choose the other box with a goat in, because he can't show you your box or the box with the car in. Therefore you will have a 100% chance of getting the car if you switch, but only if you switch, and only if you choose a box with a goat in initially.
There is, of course, a 33% chance that you will chose the car first time, then the host can show you either of the other boxes because it doesn't matter. In this case you have a 0% chance of getting the car if you switch, but only if you switch, and only if you choose a box with a car in initially.

As of this there is a 66% chance of getting a 100% chance of getting the car if you switch, and a 33% chance of getting a 0% chance of getting the car if you switch.

Just to give the other side of the story:
If you do not switch then the odds are reversed, you have a 66% chance of getting it wrong, and a 33% chance of getting it right.

In simpler terms: there is a 66% chance of getting the car if you switch, and a 33% chance of getting a goat if you switch. And if you don't switch there is a 33% chance of getting the car, and a 66% chance of getting a goat.

So I conclude that it is better to switch, as you have a much better chance of getting the car (33% more chance); assuming that you want the car, of course.
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I hope that makes sence, I tried to explain it as clearly as possible but I just worked it out and found it pretty hard to get the wording right.
seastatue
 alalex wrote: Some people say it doesn't matter because it is 50/50% chance. Others say it is better to switch door.

Hey, this proof was the basis of a "Numbers" episode already this season. You know the show with the crime-solving mathematicis professor? Wish I had saved it. Let me see if I can remember what he said...
linexpert
This depends on how you define probability.
My answer is switching the door does give you a higher chance of winning and here's why.
At the beggining you have to choose from 3 doors and only one of them have a car. This makes your chances of winning 1:3
Once the host picks a door with a goat, there are only two doors left. If you make a decision now, the chances of you winning are 1:2

In my first sentence i said it depends on how you define probability. In my reply the probability for the second choice is not at all effected by the first. For example if you have a boy and you're about to have another child, the probability of you having another boy is one in two and you don't have a higher chance of having a girl.
alalex
linexpert, you got the closest answer. Many people say 50/50, it actually sounds logical. But if you think about it, you realize that it is more complex. I just like to see people realizing that it is more like 2/3 if you switch...

And thanks for the typo thing, i meant doors and not shows...
linexpert
thanks!
Do i get any frihs?
ninjakannon
 alalex wrote: linexpert, you got the closest answer. Many people say 50/50, it actually sounds logical. But if you think about it, you realize that it is more complex. I just like to see people realizing that it is more like 2/3 if you switch...

Ummmm... that's exactly what I said, but I used percentages... and my answer was more backed up and explained than linexpert's.

In my post 66% = 2:3 adn 33% = 1:3. They are the same thing. Ok, I didn't put in the decimal places, but there was no need.
linexpert
ninjakannon, how did you put that donate link in ur sig, i don't know what my link is supposed to be
ninjakannon
The link you've got works fine, linexpert .

I asked a friend to copy the link to donate to me and then send it to me. It does work, but I can't donate to myself, so it goes to the topic that it was copied from. Therefore it will do the same with you, but it does work, I just tried it.
Sokken
Just to back up ninjakannon he got the correct answer.

it could be explained like this:

there is a 2/3 chance of getting the goat in the first place. If we get the goat first we definetly get the car if we swich because the other goat was removed.
So by swiching there is a 2/3 chance of winning the car.

2/3 = 66% as ninjakannon pointed out.
ninjakannon
Thanks for backing me up, Sokken. Greatly appreciated

I'm just waiting for alalex to reply now.