Help with Stats? Dice probability

No, the reason it is 2/3 is because you are told information about one specific face, the one face that was looked at. That is not the same at all as being given the information "B>=1".

In fact your answer is wrong, because given B>=1 the chance the card is BB is 1/2.

The faces are identical. You don't know which face is which.

Incorrect. Its a question of sampling vs selection.

If you are sampling a card at random, and then telling me "at least one side is black/white" (whichever happens to be true) then the answer is 2/3.

I read your other post but the very first answer you gave in it was wrong.

Your answer here is wrong as well.

I am very well aware of the Monty Hall paradox.

With all due respect, you don't appear to be because you are making some very elementary errors here.

This is wrong. The answer then is 1/2.

edit: I saw you replied 1/2 and then deleted your answer. This is ok, its good you are thinking about this in more detail.

Yes, because I realised that you have now changed the question to something unrelated to the OP.

You are asking a version that involves the motivation of the person announcing the information. i.e. "does the father of the child always announce Boy if he can, or does he choose randomly which sex to reveal if he has a choice", "does the picker of the card announce black if it is possible to do so, or does he randomize if he has a choice?" "We are told there is at least one four, but if the question setter had looked at a five we would have been told there was at least one five", etc etc.

That is now a totally different question from the one posed in the OP and the ones you posed subsequently, until you did a bait and switch at the bottom of page two. I realise that I answered 1/2 to a question two posts back where you mentioned something about 'unbiased selection' without bothering to read what you wrote.

That's fine, you tricked me once

The question in the OP simply states that there is at least one four (and subsequent questions are the same, until you switched things up). If all that you are claiming is that the answer to the question in the OP would be different if we are also told that we are being given this information by someone who discloses a random face that it was possible to disclose, and he happened to disclose a '4', then you are correct but that claim is so uninteresting that I wish you had come out with it a few posts ago

I flip two coins, a red coin and a blue coin. The possible results, with the result of the red coin shown first are {HH, HT, TH, TT}
I look at the coins that I have flipped and tell you that at least one of them is Tails. What is the probability they are both tails?.

x

For example, if I select all the 2 children families with at least 1 boy, the probability of 2 boys is 1/3, whereas if I select a 2 child family at random, observe that there is "at least" one boy, then the probability of 2 boys is 1/2. One is selection, one is unbiased sampling.

In both of your latest examples the probability is the same, since you are not fixing the value of one die. That is the crucial point which you seem to be missing.

For someone claiming the other person is making elementary errors, you've been wrong since your first post and Forum User has been spot on.

I find it equal parts worrying and hilarious that people think that labelling dice with numbers or letters makes any difference to the underlying probabilities.

I agree with the first bit, "if I select all the 2 children families...."

The second bit seems to me to pose exactly the same question as (1). I think what you were getting it is something I would have phrased along the lines of "I select a two child family at random. I then select a child at random, note its sex, and then announce "there is at least one X", where X is the sex of the child that I selected". Or perhaps you thought that was implicit in what you wrote, but that is not the meaning that I took from it. I simply understood it as meaning nothing more or less than that "there is at least one boy is a true statement about this family".

In any case, in probability questions if we are told some fact F, all that is meant is that F is true, that is the sample space is reduced to those outcomes where F is satisfied. We do not need to consider that we might have been told some other fact F' in some other unspecified circumstances. But usually a question like the OPs would just state "there is at least one 4", not "we are told that there is at least one 4". The former is probably better as there are no questions about the motivations of the 'teller'.

Have you stopped to consider why everybody in this thread thinks you're completely wrong?

I find it equal parts worrying and hilarious that people think that labelling dice with numbers or letters makes any difference to the underlying probabilities.

The second bit seems to me to pose exactly the same question as (1). I think what you were getting it is something I would have phrased along the lines of "I select a two child family at random. I then select a child at random, note its sex, and then announce "there is at least one X", where X is the sex of the child that I selected". Or perhaps you thought that was implicit in what you wrote, but that is not the meaning that I took from it. I simply understood it as meaning nothing more or less than that "there is at least one boy is a true statement about this family".

I said: "if I select a 2 child family at random, observe that there is "at least" one boy"

by "observe that there is at least one boy", you can equally validly assume that I either observed one child and reported its sex or I observed both children and reported the sex of one of them at random. Provided I remain unbiased on my preference for reporting the presence of either boys or girls, the answer remains 1/2.

Yes, both are the same, and both 1/2 as you say.

Do you also agree with my coin toss argument, which is basically identical except H and T replace G and B?