Before you, you can see 10 closed doors.
The host tells you: ‘9 doors reveal nothing, one door hides a Ferrari…
If you choose the right one, it’s yours !’
You think and decide to take a door.
Just before opening that door, the host stops you…
The host opens eight doors to let you see there is nothing behind those doors.
Your door is still closed and he has left one other door closed too.
Now he asks: ‘Which door do you want to open ?
The one you already choose, or the one I am offering ?’
Which door do you choose ?
For the record:
- the game host does know where the ferrari is
- the game host has done the same with every contestant and will do the same every time (that is: opening eight empty doors, etc.).
HW
ReplyDeleteI would pick the door he is offering. I would pick it because normally if someone is asked that question they would pick the one they picked first since they know the man knows where the Ferrari is, and the contestant thinks the person is trying to trick him. But really, the host knows people will think he is tricking them, so they will go with the one they already picked, even though the Ferrari is behind the door he is offering. It also makes the contestant think the Ferrari is behind the door the contestant picked when the host kept stopping him from opening it. I would pick the door the host is offering.
I’d also choose my door because at the beginning, there were 10 doors, and I picked one, and have a 10% of getting it right. He then opens 8 doors, and since he knows where the Ferrari is, he opens all the doors but the one I picked, and the one with the Ferrari. Since then I only had a 10% chance of picking the door with the Ferrari, if I picked the door he was offering there is a 90% chance of the Ferrari being behind the door.
AR
ReplyDeleteI would choose the door he is offering. Since the host knows where the car is and it’s a game show, he’s going to try and trick you. There are two ways he does this. The simplest reason is that the game host is going to be testing the confidence that the player has in his or her first choice. Second, why would a game host offer the door with the Ferrari behind it? But that’s the idea. The host is going to offer the door with the car behind it and the player will think the host is tricking them into that door.
In the game, you start out with a 10% chance of choosing the correct door. Then the host then takes away 8 doors. The door that you choose still has a 10% chance of having the car behind it. This means that the door the host left close has a 90% chance of having the Ferrari behind it. It has 90% because it has to take the percentage of the other doors. The correct choice is the door that the host offers.
TM
ReplyDeleteI would pick the door he is offering. The host knows that most people would think he is trying to trick them, so they will pick there door because that in other words would trick the host. The host knows this so he will make it so he isn’t trying to trick you. He is tricking you into to thinking you can outsmart him, in other word he is making you think you are one step ahead. In reality though, he is one step ahead of yours. He is testing your self confidence in yourself with your decision. He knows that you know that he is trying to trick you, so if he made it so you were actually right you will always pick the wrong door because you will doubt yourself. As he takes doors away the probability of getting the car goes up. The probability of getting the car goes from 1/10 to 9/10 .This would cause you to even more so doubt yourself because you think he is trying to trick you. You might even think the car isn’t behind either of those doors. You know that nobody ever gets the car and you do the opposite that you think the host wants you to do.
E.R.
ReplyDeleteI would choose the door the door I had in the beginning. This is because the host knows which door the car is behind and wouldn’t want to lead me to it. The probability of me getting the car was one out of ten in the beginning. After he opened the eight doors, the probability was fifty fifty. As seen on other game shows, hosts don’t want the contestants to win. This would mean he would lead people away from the prize.
A.L.
ReplyDeleteThe percentage of a chance that you could get the possible Ferrari is 10%. I say this since there are ten doors (even if 8 are open and 2 remain closed) and one of those ten doors reveals a Ferrari. The door I would choose would be the door he isn’t offering. The reason I say this is because this is you’re original answer and you now have a 50% chance of winning the possible Ferrari. Also the host didn’t open you’re most recent pick, and offered you the question instead of just letting you open you’re pick.
E.A.W.
ReplyDelete10/8/10
I would choose the door that I chose before hand because the probability of me choosing the correct door is 5/10. I would decide that because at first there where 10 doors and the host had eliminated 8 of the doors I would have had a 1/10 probability of winning. Now that there were only 2 doors, my probability of winning the Ferrari would increase to 5/10. I know that the host knows where the Ferrari is, and he probably is using his last defense to keep me from winning. His door could also be correct, considering that he knows which doors do and do not have a Ferrari behind them, but this is a game show where they don’t exactly want the person to win. So, I would choose my door because I do have a 5/10 probability of winning and go against my doubts.
JD
ReplyDeleteIf this situation came to me, I would most likely go with the door that I picked because chances are, the door that he picks is likely to be empty. The probability for the chance of your door has gone down 1 for each door the man revealed, making the chances of you getting the Ferrari. For example, before he revealed any doors the chances were ten percent for him to get it, after he opened one door the chances increased to eleven point one, then twelve point five, then fourteen point twenty-eight, sixteen point six, twenty, twenty five, thirty three point three, and lastly, at our point, fifty percent.
RT
ReplyDelete10/8/10
Door Question
P-6
I would switch to the other door that the game host didn’t open. I would do this because I first had a 1/10 chance to pick the right door. Every time the host closed a door the chance of choosing the wrong door goes down by one. For example every time the host opened a door the probability would be 1/8, 1/7, 1/6 and it still goes down by one. If I had switched my door to the one he had not opened after he opened the 8 than I would have a ½ chance of winning the right door.
MJS
ReplyDeleteIf I was the contestant I would choose the door I already have. I’d choose my door because if the guy already opened 8 out of the 10 doors that are not yours than that means you have a 50-50 chance. When you picked the one door there were still 9 doors. You only have a 10% chance of getting the car, but he opens 8 doors to give you a 50% chance. Since he didn’t tell you from the start you lost meant that you could have a good chance.
MF
ReplyDeleteThe door I would choose is the door I have had since the beginning. This is because since the host knows which door the car is hidden behind He would probably want to lead me away from it. Before the host had opened the eight doors, the probability of winning this brand new car is 1 out of 10. Now after he has opened the eight doors have been opened and there are only two left. This chance is 50-50. As seen from other game shows, the host wouldn’t want to give the car (or what ever the host is giving) to anyone. This would mean he would want to lead the contestant away from winning the car.
E.R.
ReplyDeleteI would choose the door the door I had in the beginning. This is because the host knows which door the car is behind and wouldn’t want to lead me to it. The probability of me getting the car was one out of ten in the beginning. After he opened the eight doors, the probability was fifty fifty. As seen on other game shows, hosts don’t want the contestants to win.
RT
ReplyDelete10/8/10
Door Question
P-6
I would switch to the other door that the game host didn’t open. I would do this because I first had a 1/10 chance to pick the right door. Every time the host closed a door the chance of choosing the wrong door goes down by one. For example every time the host opened a door the probability would be 1/8, 1/7, 1/6 and it still goes down by one. If I had switched my door to the one he had not opened after he opened the 8 than I would have a ½ chance of winning the right door.
J.M.
ReplyDeleteI would choose the door that I picked. My dad always tells me to stick with my first choice. Most of the time my first choice is right. Also he already opened the other doors. That leaves only two doors left. That is a 50% chance to get a new car. If you choose one of the doors that are open only a 10% chance of getting a new car.
ZGB
ReplyDelete1. I would open the door that the host had picked because he would be increasing my chances to win the Ferrari with each door he opens. There is a 50/50 chance that my door would have a Ferrari behind it, but he has tried this trick on every guest, and if I had thought to pick my own door, so would have every other guest. Since the host has experience, probably 90% would pick their own door in risk of being tricked by the host. Since he had tried this, he expects me to pick my own door because of this fear of losing and being tricked. So, because of this mind-trickery and percentage of losses, I would pick my own door.
LG
ReplyDeleteI would choose my door because the host is most likely trying to trick if you are picking the correct door. Also I like the options in being a 1/2 chance instead of being a 1/10 chance and a 1/2 is way better than a 1 out of 10 chance of getting it. But still if he takes away all of the chances he is most likely trying to trick you so he makes you think witch door you want and he is trying to put pressure on you. Also you would have to go back to the contestants he gave them a 1/2 chance and think and if they all chose the other door and they got it wrong that’s another reason why you should pick the door. Also the probability of getting the door correct is higher and with the probability being higher so does the chance of getting the right door.
A.W.
ReplyDeleteI would choose the door the host has left other than the door I have chosen. That is because the probability of me getting the right door is 10% chance with all the ten doors. But when eight doors are gone there is a 50% that I will pick the right door. On the other hand the host has a 100% chance he will get the right door, which is he will get the door right. Also the host does know which door the Ferrari is in. so thus he will have the right door to open.
C.S
ReplyDelete10/8/10
If I were a contestant on the game show, I would choose the door that the game show host offered me, because he could higher the probability of me choosing the right car since he knows which door has the car behind it. It actually depends whether or not the game show host wants me to get the door with the car behind it, or not. At the end with the last two doors, the probability of me choosing the right and wrong door is 50% for both. Since I began with a total of 10 doors, the probability of choosing the right door decreases, but when it comes down to the last two doors, the odds of me choosing the right door increases. Just like on a linear graph, the data would create a line, but from the information of the door possibilities, the line would decrease
AWM
ReplyDeleteI would choose the door the host offered. I would choose the door the host was showing me because the host knows which door the Ferrari is behind. Also because the host is going to pick the door with the Ferrari behind it if you didn’t pick that door. Therefore you have a 10% chance because there were 10 doors.
SK
ReplyDeleteDoor Question
10/8/10
Period: 6
If I were in this situation, I would choose the door I did not originally choose. Based on probability, I had a 1/10 or 10% chance to pick the correct door, and a 9/10 chance or 90% to pick an incorrect door when all ten doors were open. However, when he closes all of the doors but two I have a ½ or 50% chance to pick the correct door, and a ½ or 50% chance to pick the incorrect door. Based on this, switching doors increases my chance to pick the correct door in order to get the Ferrari, while the chance to pick the incorrect door decreases. Even though the location of the Ferrari never changes, when you close a door the chance you miss the Ferrari goes down by one, while the chance you will find the Ferrari stays the same. ½ chances are far better odds than 1/10, which are the odds when you choose the first door. For this reason it is more likely for you to find the Ferrari when you switch to the other door.
WO
ReplyDeleteDoor Question
10/8/10
Period: 6
If I were in this game show, I would choose the door that I did not originally think about choosing in the two that are closed. I would do this because I first had a 1/10 chance to pick the right door and a 9/10 chance to pick an incorrect door. After the host closes all of the 8 doors, I have a 5/10 chance to pick the right door and a 5/10 chance to pick the incorrect one. If I switch my choice of doors to the other door that I had not thought about picking, the chance goes to ½ of getting the Ferrari. Every time the host closes a door, the chance of you choosing the incorrect door goes down by one. The probability of ½ is better than the probability of 1/10.
RT
ReplyDelete10/8/10
Door Question
P-6
I would switch to the other door that the game host didn’t open. I would do this because I first had a 1/10 chance to pick the right door. Also, I have a 9/10 chance of picking the incorrect door. Every time the host closed a door the chance of choosing the wrong door goes down by one. For example every time the host opened a door the probability would be 1/8, 1/7, 1/6 and it still goes down by one. If I had switched my door to the one he had not opened after he opened the 8 than I would have a ½ chance of winning the right door.
TM
ReplyDeleteThe boys are getting just under 50% savings for their meal. The equation to get the total for the combo meals is p(1.0825)(1.15)+(p)(1.15)-p. Since the tip is applied to both there is no way they could get exactly 50% off because you are paying something for both. If they were paying the same amount of extras for both beyond the price they would be getting exactly getting 50% off. The exact percent they are getting is 44%. I found this by using by plugging number is for P and then dividing the final cost of both by the cost of just the first one, in essence the change of cost between the one they are paying sales tax on and the one they are not.
AM
ReplyDeleteThere are 10 doors and he tells you to choose a door. Then you choose a door to win the Ferrari. So the guy shows you 8 doors that are empty and since there are 10 doors total and he/she has showed you 8 doors that are empty that means you have a 10% chance to get the Ferrari that is behind the door you chose, and there is a 90% chance to get the Ferrari behind the other door. Also he will try to convince you to choose the door that could have the Ferrari behind it so you want to choose the door that he try’s to convince you to choose.
MB
ReplyDeleteBefore the host opened any doors, there were ten doors closed. When all doors are closed the chances of you picking the right door would be: 5%. When the second door is opened you have a 10% chance of picking the right door.
3rd door opened: 15% Chance.
4th door opened: 20% chance
5th door opened: 25% chance
6th door opened: 30% chance
7th door opened: 35% chance
8th door opened 40% chance
Now there are only two doors left. The chances of getting the car would be 40-60. I would go with your instinct and chose the door that you had originally leaned towards.
LG
ReplyDeleteI would choose my door because the host is most likely trying to trick if you are picking the correct door. Also I like the options in being a 1/2 once the eight doors are open chance instead of being a 1/10 chance when all doors were closed and a 1/2 is way better than a 1 out of 10 chance of getting it. But still if he takes away all of the chances he is most likely trying to trick you so he makes you think witch door you want and he is trying to put pressure on you. Also you would have to go back to the contestants he gave them a 1/2 chance and think and if they all chose the other door and they got it wrong that’s another reason why you should pick the door. Also the probability of getting the door correct is higher and with the probability being higher so does the chance of getting the right door.
C.D.
ReplyDeleteThere is a 9 out of 10 percent chance (90%) that you will pick the right door. so I would pick the door I already picked because I picked it and out of the 8 doors it still has the Ferrari in it but out of 9 doors it still has the Ferrari in it but with 10 doors you will most likely get the Ferrari because all they did was add another door.
And either way you will have a 9 out of 10 percent chance of getting the Ferrari because if you add up the doors that have nothing behind them you have a 9 out of ten door chance of getting the Ferrari.
Jd
ReplyDeleteIf this situation were to occur to me, I would choose my door because the probability of it being my door, even after he opens the others, is still ten percent. I got information by taking the hundred percent we started with and taking ten percent every door opened. The reason I chose my door is because either way, it’s the same chances of you getting the Ferrari.
AWM
ReplyDeleteI would choose the door the host offered. I would choose the door the host was showing me because the host knows which door the Ferrari is behind. Also because the host is going to pick the door with the Ferrari behind it if you didn’t pick that door. Therefore you have a 10% chance because there were 10 doors.