What is the automatic answer?
I think that there is a 50/50 chance that the door you are on will have the car.
After he has opened up one door: there are 2 doors, one has the car the other doesn’t. 1/2=50% for the car at the 1st door and 1/2=50% at the 2nd door.
I think that there might be some information missing. At the very start of the question there is 2/3 chance that the door you choose will have the goat and 1/3 that it will have a car. but after he opens one for you, it should be 50/50.
“What is the automatic answer?
I think that there is a 50/50 chance that the door you are on will have the car”
You answered your own question
It is not 50/50, it’s 1/3 if you stay, and 2/3 if you change. You can think of it like this:
Originally, there is two groups, “the door you picked”, and “the doors you didn’t pick”. Now, “the door you picked” has a 1/3 chance of having a car behind it. “the doors you didn’t pick” have, as a group, a 2/3 chance of having a car behind one or the other. So, when one of the doors from “the doors you didn’t pick” is opened, then “the doors you didn’t pick” (the one you can switch to) is the only member of the group, and still holds the 2/3 value as the group, and consequently, by itself. I couldn’t explain it to myself once I knew the answer, but I wrote a little computer simulation to go through the whole thing with random choices, and sure enough it was true. After coding the simulation, it started to make more sense to me this idea of “grouped chances” even though I don’t know what the correct name for that is.
Sorry, I still disagree.
Well call the three doors 1, 2 and 3 respectively.
Say you pick 1
Then you say that 2 and 3 have 2/3
The person opens 3 with the goat
That leaves 1 and 2–>you say 2 has 2/3 well at the start that would mean 1 has 1/3, 2 has 2/3 and 3 has 1/3 (or 2/3 don’t know which one you would choose) 1/3+2/3+1/3=4/3, 4/3 doesn’t =1<–
You say 1 has 1/3 and 2 has 2/3
Well say if you had picked 2 at the start then 1 would have a 2/3 chance and 2 would have a 1/3 chance
The act of you picking a door can’t have any effect on the chances. But the way you say it suggests that it does.
How does the act of picking a door change the chances? It shouldn’t and it doesn’t.
There are 3 doors each have a 1/3 chance
Then there are 2 doors each have a 1/2 chance regardless of which one you pick.
I think that the book you got it out of is wrong
I don’t know how you did the computer program, but it seems wrong to me as well.
I hope you can understand all this and can see where you went wrong or where the book went wrong
Yeah, I agree with alex. The way you explained it made sense for a second but then it’s just like “Wait a minute …”
Sure there are three doors, that means there’s a one 1/3 chance that the door you pick has the car behind it. And once you pick one that has goats behind it, then there’s only two doors left. One has a car one has a goat. There’s 1/2 chance there’s a car behind either one. Fifty percent. Now that the other door has been chosen, it’s like it never existed. You shouldn’t even be thinking about it anymore.
I mean, if you only have a choice of two doors, its not Out of 3, it’s out of 2. Maybe you forgot to tell something?
It is my experience that if you tell people the answer to it within about 30 minutes of telling them the riddle, they believe you. Any longer, and it takes a lot more explanation, more and more as time passes.
Another way to explain this is to lay out all the possible things that could happen given an arrangement of things:
door 1: car
door 2: goat
door 3: goat
Then there are the following siutations where someone can pick the car:
door1->stay
door2->switch to 1
door3->switch to 1
and the following situations where someone can pick a goat:
door1->switch to 1 or 2
door2->stay
door3->stay
Notice that in the car category, 2/3 are “switch” and, only 1/3 stay.
If that isn’t convincing enough, I will try and find some external sources of explanation.
In other words before the person opens a door there is a 2/3 chance that you are wrong and a 1/3 chance that you are right
This is the same as the goat category
Have a look at this after the the person opens up a door with a goat
door 1: car
door 2: goat
door 3: goat -->has been opened
Then there are the following siutations where someone can pick the car:
door1->stay
door2->switch to 1
and the following situations where someone can pick a goat:
door1->switch to 2
door2->stay
There is a 50% chance that they will pick the car and 50% that they will pick the goat. Everyone, tell me if you agree, and perhaps you can explain it better than me.
There are others. On the websites themselves I am sure there are links, and if you want to search for yourself you might type in “monty car goats” into a search engine.
“Well, what did I think, first? I too thought that the solution was obvious, but I did not tell this to Anya. I pretended that I knew the correct answer from the beginning, of course.”
My head and tail both equal are,
My middle slender as a bee.
Whether I stand on head or heel
Is quite the same to you or me.
But if my head should be cut off,
The matter’s true, though passing strange
Directly I to nothing change.
What am I???
I understand where you have been coming from now, but…
We don’t know if this is at random or not, you should have said that the person can only choose a door that has a goat. And that he couldn’t pick the door that you are on. Say if you picked a goat and then the host showed you behind your door. You be better off changing because you know there is a goat behind your door.
I understand the problem better now and this quote from the first site you gave might help others
2/3 because 2/3 are wrong doors and 1/3 are right.
Sorry alex. The trick with this one is phrasing it just right: a little bit of mis-phrasing can cause a cascade of mis-interpretation that just destroys any possibilty of understanding the problem.
A man and his son were on a tour of an atomic power plant. In the control room, the boy asked if he could see the controls for the reactor core. The head physicist said yes, and explained how the controls worked. After the boy left, the head physicist turned to an assistant and said, “That was my son.”
How could that be?
You are stuck in an air tight room. You only have 15 minutes worth of oxygen left. There are no windows, there are only two doors. And in this room there are 2 computers, one is programed to tell nothing but the truth. The other is programed to tell nothin but lies. You can ask ONE question to ONE of the computers. If you touch the wrong door both of them disappear and your stuck.
A snail fell down a hole.It is 30cm deep, and the snail trys to escape as fast as possible.It goes up 13cm every day, but the following night it always has to sleep (and dream g) and slides down 7cm.
How many days does it take the snail to get out?
