### Monty Hall Problem

**You are on a gameshow and the host shows you three doors. Behind one door is a suitcase with $1 million in it, and behind the other two doors are sacks of coal. The host tells you to choose a door, and that the prize behind that door will be yours to keep.**

**You point to one of the three doors. The host says, “Before we open the door you pointed to, I am going to open one of the other doors.” He points to one of the other doors, and it swings open, revealing a sack of coal behind it.**

**“Now I will give you a choice,” the host tells you. “You can either stick with the door you originally chose, or you can choose to switch to the other unopened door.”**

**Should you switch doors, stick with your original choice, or does it matter?**

I would stick with the door I have chosen because its a 50% chance of being coal or $1 million so I would stick with my door I have chosen and just have faith in my door.

Ok. So the game host helped me out with 75% and gave me 50%. Now I can get coal or 1 million dollars 50/50. I don’t think that it matters witch box i choose because I could get coal or 1 million. It’s the same percentage if I choose either.

It does not matter because you don’t know where the money is at so you can’t do anything.

Where is your math evidence that supports your decision?

It doesnt matter which door because since the host eliminated one door so theres a 50/50 chace you will pick the right door .

I would switch doors because theres a 50% chance of getting the $1 million and also getting the coal so i would switch the doors and pick another door.

the probability of getting the 1 million dollars is 1/2 after you open the first door. so technicly speaking it doesnt really matter because you only have a 50% chance of getting the 1 million dollars. so it doesnt really matter to me!

well it does matter to where you move it.

Where is your math evidence that supports your answer?

I think that you should keep the door you picked because since there are two doors and one of them has money and the other has coal so it would be a 50% chance that it is money and a 50% chance that it is coal so it dose not matter what choice you have because it is a 50 50 chance.

I THINK IT WOULD BE BETTER IF YOU GET 50 50 CHANCE THAT YOU WILL GET A BETTER CHANCE

So….should the contestant stick with the original choice or switch doors?

It doesn’t matter because, it’s a 50 50 chance of what you’re gonna get. The probability of the choice is 50 50. So I might as well stick with same door because, the other one might have coal. Of course, this door might have coal to.

stick with your original choice cause maby the host is just trying to mix u up and if the host opened one with coal on it than its for sure not the one he picked

What is your math evidence that supports your decision?

It does not matter unless you can see through walls because it is a 50/50 chance to get coal or to get money its going to be about luck for the person.

It does not mater now because there are 2 doors left so there would be a 50/50 of getting the door with the 1 million dollar’s behind it.

I think it doesn’t really matter what door you pick because the probability of getting coal or money is equal since the host opened one door already. It is a 50-50 chance (50%)

It doesnt matter what door you pick since the host already opened one door the chance of getting coal or money is equal its a 50/50 chance.

i think there is a 50/50 chance that he will pick the door with the money now because there are only two more doors left. so each door will have a 50 percent chance. the reason they will have a 50 percent chance is because the percent has to equal 100 and 50 /50 equal100 since there are only two doors left. so his chance is that he will most likely pick the right door and get the money…

keep with the choice you had before because you have about a 50% of you getting the million dollars then you not getting it.

I would stick with my original choice because its a risk I would take because you don’t know what you could get.

What is the math evidence that supports your decision to stick with your original choice?

He should stick with his original choice because if he were to pick the other door there is a probability it would be coal or a million dollars and the magic man already opened one door with coal so theres about 50% chance he will get coal and 50% he will get the million dollars.

He should stick with the door he first chose becuase there is a 50 out of 50 chance that one of the doors will be filled with cole so it doesent matter wich one he chooses its determined by chance

It really doesn’t matter because you can either chose the one with the coal or the money either way. I would stick with my original choice.

Where is the math evidence that supports your decision?

It doesn’t matter, because there is an equal 50% chance of winning if you pick either one of the doors.

I don’t believe it matters b/c u don’t know the other 2 doors

also b/c its a 50% chance u will get $1 million

It doesn’t matter because it has a 50, 50 chance and no matter what he chooses it could be the money or not!

what i think is it wont matter because it is a 50/50 chance of getting the money.

it doesnt reeally matter if you switch doors becuase either way you have a 50/50 chance of getting coal and of getting the 1 million dollars so it doesnt really effect anthing if you change doors.

I would have sticked with the original case because the PROBABILITY of getting that money…..would be 50% amd or likely as not…what would I do with that money……um…..Id pay so teachers could get a raise…..only cause I love you!!!!

Darn! If only this blog question was a real life experience! ðŸ™‚

skylarr2014

well it doesnt matter cuz there will still be a 50 50 chance

I would switch doors because let’s say that you have 20 doors and you choose door 6. Then the host opens 18 doors, all with bags of coal and the only door left is door 14. You’d obviously have to switch doors . This is because the door you chose first is 1/20 and the rest of the probability is 19/20. Once you chose your door, and the host opened the other 18 doors, door 14 is the new 19/20 . So if I choose door 1,it would be 1/3 and the other 2 doors would obviously be 2/3. Then he opens one of the doors and the other door is the new 2/3. You would have 2/3 chance if you switched to the other door, and that’s more than if you stay on your original door.

I like how you tried to relate this problem to a similar problem; however, it seems like you might have confused yourself. Once a door is opened, does it change the probability for your current choice?

yes

3 doors and there’s only $1million behind 1 of the doors. You chose 1 of the 3 doors then the host opens one of the doors but not the one you chose, and behind that door there are sacks of coal. Now there are only 2 doors left, 1 with coal and 1 with $1million, so now you have a 50-50 chance of winning 1million or sacks of coal. Do you stay with your original door or change it. In my opinion I would stay with the same door cause if you were lucky the first time on not choosing the wrong door then the door that you originally choose would be the better door.

I would honestly stay silent for a while, because theres 1/3 of a chance that ill get the proper door. Since one of the doors has been opened to reveal the sack of coals, i would have 1/2 of a chance to get it properly. It doesnt really matter, but what matters is choosing the correct door.

So yes, i would have a 50/50 chance of getting the money, OR a sack of coals.

i think it doesn’t matter you can chose either because now you have a fifty,fifty chance of win or losing. if it was me I would go with my original choice.

i would chose to open the other door because now you have a more likely chance to win the million dollars

What is the probability of winning the million dollars? Does this knowledge change your thinking?

If I were the person, I think I would have stuck with the one I choose and see if my luck was good. But it doesn’t matter because you always have what you get.

Is there any math that would support the decision to stick with your original choice?

I say stick with your original choice because this is kinda like a test and so people say to always stick with your original instinct because it is usually right.

Is there any math that helps you decide whether it makes sense to stay with your original choice or to make a switch?

you should stay with the same door because there is no differince because i am not on the game show

Jason,

This response does not show that you understand any of the math we have been learning? Is there anyway you can tie probability into the choice the contestant should make?

Even though there are more doors that have coal before he opened one there would have been a more possibility of opeNing a coal one now it’s a 50%,50%chance I say stick whit the door you have

If I was a contestant at a game show I would stick with the door I had already chosen because when the host showed the sack full of coal it is automatically a 50-50 chance for either the 1 million dollars or the sack of coal. So either side I choose it will all depend on fate! lol

It does not matter if you switch what door you chose originally because you don’t know which door has what in it. One of the doors has coal and the other one has the money since the host showed you one of the doors that had coal in it, so you have a 50% chance of getting either one of the prizes. You can switch doors, but there would be no point because you can’t know which door has what prize inside.

It doesn’t matter because one of the two remaining doors is full of coal and the other has the money so there’s a 50-50 chance the door you picked has the money or not.

It does not matter if you switch doors or stick with the original answer. The probability is still one in three.

Does the probability change once one door is opened?

Most people will say that it matters which door you choose because you could win $1 million. In all honesty you don’t need money, so I would stick with the door I chose. Plus, its a fifty fifty chance, so I could get the door with the money or the door with the coal.

It doesn’t matter what door you stick with or switch to because either way, it’s still a 50 50 chance to choose a door with one million dollars or a sack of coal, so it doesn’t matter if you switch or stay with the original door.

yes you have 50% chance of getting the million and a 50% chance of getting coal so you should go for it.

What do you mean “you should go for it”?

It does not matter because ether two of doors can have money or coal ,also because the host only opened one of the doors so theres no real chance if he knows what door because he still doesnt know what door

Does probability play into your decision at all?

it does not matter because there is a 50-50 chance that you would get the money or the other bag of coal. i know this because there are two choices and one is the money and the other is coal.

It doesn’t really matter as it will be a fifty/fifty chance you’ll get the money or coal.

I think that you should stick with the same choice!

Why? Where is your evidence?

I would switch because there is now only 50/50 chance and I think that it in way s just luck

If the probability is 50% money, 50% coal what would make you switch?

You should stick with the same door because it still is a 50/50 chance that the money is behind one of those doors. Since they already revealed one of the doors that have coal that means one has coal and the other has the money, so it wouldn’t matter which one you choose.

I think that it doesn’t really matter. You don’t really have any way of knowing if you will get the money or the coal, so it doesn’t really matter. There is a fifty-fifty chance of you getting the money. If you switch, then you might get either one. There is no telling which ine you will get. You should just trust your instincs. If you get the money, then you get the money, if you don’t then you’ll just stay the same as when you started, so you don’t lose anything. (Besides your only chance to get a million dollars.) So really, if the chances are equal of getting either one, then it doesn’t matter which one you pick.

You should switch doors because what is a sack of coal going to do you would see that there is only 2 doors left and one would have the million dollars and the other would have coal and what you would see is in what different orders could the doors be in and you would see which fraction would be bigger and after you see which fraction is bigger you would switch to that door and win the one million dollars.

Thanks Kevin but what you have said is a bit confusing? Does probability play into your decision at all?

When there were three doors to choose from there was a 1 in 3 chance or 33.33% probability that i would pick the million dollars. After he opened the door with the coal behind it i then had a 1 in 2 chance or 50% probablity of picking the door with the million and the same for the door with the coal so it doesnt really matter if i change doors or not so i am going to go with my gut and sick eith my first choice.

It wouldn’t matter bEcause u have a 50%chance of getting the 1 million and something else.

First I think you should keep the door you picked. I think you should because since there’s two doors one of them has money and other has coal. Then it would be a 50-50 chance that it would be the coal or the money. So in other words I think you should just keep or stick to the door you picked.

it would be a 50/50 chance of either getting the coal or the money.

So it would not matter. so I am going to go with my heart an stay with my first choice.

I think that I should keep the same box because it is a 50/50 chance of you losing so you it is just risk it.

It does not matter because it doesn’t say oh the right one has a sack of coal it just opened one so which ever one we choose we wouldn’t know between the first or second or third anyhow.

I don’t think it matters because you have a fifty-fifty chance of winning or losing. so, I would stay with the original choice.

with one of the doors eliminated there is a 50-50 chance that there will be the sack of coal in ether of the doors

i would think that it doesn’t matter, you can choose either. because you would now have a fifty fifty chance of wining or losing. so i would just go with my original choice.

I think that you should stay with your choose because you have 1/2that she will get the right one

It doesn’t matter if you stick with the original choice or switch doors because the 50 50 chance that there is $1 million behind a door. So you should stick with the original choice.

first it was 1/3 of a chance to get $1,000,000 then 1/2 of a chance

to get the money. to me it really doesn’t matter what you do it’s all

based on luck

I think you should stay because it does not matter what you pick because it a 50-50 or 50% chance of you the money. You should stay with the case you have.

I would stick with the door i have because the sack of coal was the door he opend so you have more fo a chance to get one million dollars with the door you have.

To be honest with you it really doesnt matter because either way what matters is that you got to play on the show.

I would stick with the door because there’s a 50-50% chance that the door he picks has money or coal. It doesn’t matter what you get because you might get a door with coal or money . The person that had him choose a door might eliminated the door with coal or money.

IT DONT MATTER!!!!!!!There’s a 50 50 chance that you’ll either get a sack of coal or the million dollars you have to have luck…..but I would stick to my own door (Not part of the answer but just sayin):)

You should stick with the same door because there will be a 50-50 chance you will get a sack of coal or a million dollars. Since one door was picked that means that you have two door and a 50-50 chance to win the million dollars. I think it wouldn’t matter what door you choose.

You have a 50/50% chance to get coal or 1 million dollars it doesn’t matter what door you choose because, you are more likely to choose the wrong door.

i think that it doesnt matter witch door you pick because the probablility of you getting coal or money is equal to eachother since the host already opened one door. so it is a 50-50 chance.

I will stick with the door because whats coal going to do and if you stick with the doors you will still be with the 1milion