Women, math, and the Monty Hall problem

[IndigoChild5559]

Also, there is never a consequences of the 1 of 3 door option. So it is simply an irrelevant bit of theater.

What do you mean? The consequences are: if you choose the right door, you get a fabulous sexy car, and if you choose wrong you get a stupid goat that you don't want.

 

[IndigoChild5559]

There was no “system”. Just some irrelevant theater before the actual choice.

Riiiiight. The world is random. Probability doesn't exist. Math is a farce. 2+2=5 or 9 or 7 million. You never know when you open your front door in the morning whether the sun will be green or not. Got it.

 

[We Never Know]

Okay, let's try it one post at a time. There are 3 doors, A, B and C. Behind one of them is a car, and behind the other 2 is a goat.

You have to pick a door -- so please tell us which door you've chosen, and what you think the chances are that it has a goat behind it.

(To prevent my cheating, there's a way to show how I chose which door to put the car behind, but I'm keeping it secret for now.)

It relies on the 3 doors staying in the equation..

I pick door B. 33.3% chance. 1of 3
You shown me a goat behind door C.

You now offer me a chance to switch my door(switch from B to A) that gives me a second choice(66.6% of three doors because I can pick another choice) (I am already up 33.3% of three doors because you have shown me door C is a goat)

However once door C is eliminated its a two door choice. I can stick with door B or change to door A. Since door C has been eliminated it is a 50/50 now.

It can be argued all night but it is what it is.

 

[blü 2]

Your not following.

First, what do you mean "at no stage of the game are the true odds ever 1 in 3"??? Perhaps I'm misunderstanding you, but this is just basic elementary school probability. Second, when you made your first choice, you had a 1/3 chance and that doesn't change just because one door is opened.

Thinking out loud:

I have an initial choice of 10.
I choose 1.
8 blanks are removed, leaving my original choice and the last remaining 1.

What are the odds in play at this point, do you say?

Are they difference to the odds in play before I chose?

 

[IndigoChild5559]

It relies on the 3 doors staying in the equation..

There are still 3 doors. It's just that one is now open. But there are still three doors in the equation. You are making the same mistake I originally made. And we were both wrong.

 

[Evangelicalhumanist]

My friend, it has nothing to do with psychology and everything to do with math. I'm very sorry that you didn't understand the math reasoning; not everyone will.

Well, it's a little bit of both, actually -- because there is a change of reference between the contestant's first and second choice. The first choice is:

Guess which door the prize is behind -- this choice has a 1 in 3 chance of being correct.

The second choice is very different: it's not, now guess which (of 2) doors the prize is behind, because your first guess hasn't been answered yet -- it's still in play. No, your second choice is: Guess whether your first guess was right or wrong. That is a very different thing.

And, of course (as you pointed out long ago in your OP, the odds that your first choice was wrong is 2/3 -- and absolutely nothing has happened since to change that. Nobody has moved the car or the goats, so 2 out of every 3 times, if you don't switch your answer, you will be wrong.

 

[We Never Know]

There are still 3 doors. It's just that one is now open.

Its been eliminated. There are two left.

But there are still three doors in the equation. You are making the same mistake I originally made. And we were both wrong.

At the point when Monty asks if you want to switch, only two doors now matter. At that point it is a 50/50.

Keeping all three doors in play you had a 2 of 3 chance. Monty gave you a door for free and you get to switch a door. It will always be this way because Monty will always open up a goat from the start.

Btw, on the newer Lets Make a Deal, you dont get the option of switching when, as always, you are shown one without the big deal from the start after you've made your choice.

 

[Revoltingest]

Simplest way to see it.
There are initially 2 groups.

Group A - The door picked 1st.
1/3 chance of the car.

Group B - The 2 other doors.
2/3 chance of the car in this group.

Sequence:
1) I picked Group A. 1/3 chance of a car.

2) Monty shows me 1 door in Group B has a goat.
This is new information about Group B.
I now know which door is a goat.
The other could be the car.
Group B still has 2/3 chance of the car.
But only the non-goat door has this chance.

 

[Heyo]

We can agree to disagree.

Maths is neither a field of majority decision, nor is it aesthetics.

The Monty Hall Problem has been solved. The experts all agree, experiments have been made, and they agree, too.
But people here argue as if all that doesn't matter. It's not that they say, "I don't understand the solution", they actually argue against reality.

"Facts don't matter, I have my alternative facts", is exactly how YEC, climate change deniers and Trump voters can exist.
If you are not a YEC, not a climate change denier and not a Trump voter, but you insist that you've got a 50/50 chance when you switch, you operate on the same level as those three groups who are denying reality. You have no trust in science or experts. You only ever have a maximum 50/50 chance to be on the right side of any subject, you were just lucky with YEC, the climate and Trump.