You are an overconfident ignoramus. Thanks for demonstrating the Dunning-Kruger effect so impressively.
The reason for having BG and GB is the fact that it's twice as likely to occur than each of GG and BB.
The reason for having BG and GB is the fact that it's twice as likely to occur than each of GG and BB.
In GB and BG, he has only one way of telling you which is the boy. In BB, he has two. Thus, four possibilities a) GB, b) BG, c) BB and he gave you the first, d) BB and he gave you the second.
Your brain will of course refuse to process the above due to your earlier remark and the sweet, sweet motherfucking irony it would mean.
Not recognizing the difference is what lets some poker players make money.
Consider this question. A chap flips a coin in the morning and thereby chooses one of his two children. Today he will only talk about that child. Later I meet him and he talks about his son. I thereby deduce that he has at least one boy. What are the chances he has two sons? (corrected in edit - thank you)
Answer: 1/2.
Another version: I meet a man and his son, and in conversation it emerges that he has two children. I can see he has at least one son, what are the chances he has two sons?
Answer: 1/2.
Another version: I meet a man and it emerges in conversation that he has two children. I observe that he is carrying a shopping bag with a child's dress in it, from which I conclude that he has at least one girl. What are the chances he has two girls?
Answer: 1/3. (I had to change gender because I couldn't think of anything that would be specific to a boy.)
Your dismissal of the idea that there are other interpretations than your own is disappointing. The language in which you couch your dismissals even more so. Are you like this in person?
Do you mean "what are the chances he has two sons, not children?
By the way, thanks for your input on this thread, I'm sure I speak for many in saying that I really appreciate it!
> Do you mean ... "sons," not "children"?
And thanks for the kind comment.
The two are independent variables, man. I don't know how to explain it any more clearly than that. What's tripping people up is the idea that removing GG from the possibilities doesn't affect the local probability of either particular child being girl. It does. You must reformulate. THAT's the counterintuitive part. It's just hella hard to explain, because there are too many 2's and 1/2's floating around the problem, so when you say one cancels another, people think you're not incorporating the first to begin with, so you must be one of the dolts the author is trying to learn some knowledge.
The following, you can take or leave: probability is my thing. I got Monty Hall right when I was in 6th grade. I was an AIME invitee, if you know what that is. I got 800 on the math SAT; 36 on the math ACT in freshman year. None of these things mean anything, logically speaking, I know. I say them only to encourage you (and only you, because you're putting in effort) to consider what I'm saying as fully as you're considering what the crowd is saying.
> No. In person I can see what the other party is thinking.
> The two are independent variables, man. I don't know
> how to explain it any more clearly than that.
> What's tripping people up is the idea that removing GG
> from the possibilities doesn't affect the local probability
> of either particular child being girl. It does. You must
> reformulate.
> It's just hella hard to explain, ...
> ... you must be one of the dolts ...
> The following, you can take or leave: probability is my
> thing. I got Monty Hall right when I was in 6th grade.
> I was an AIME invitee, if you know what that is. I got
> 800 on the math SAT; 36 on the math ACT in freshman year.
> None of these things mean anything, logically speaking,
> I know. I say them only to encourage you (and only you,
> because you're putting in effort) to consider what I'm
> saying as fully as you're considering what the crowd is
> saying.
I mention these things only to point out that you might consider that you are wrong.
So, do you answer 1/3 for each of A, B, and C?
>"The two" ?? What "two"? Your "explanations" are very unclear.
The only two there are: the two children. The sex of one is independent from the sex of the other.
>You will find many things difficult if you don't learn how to slow down, take time, be precise, and explain clearly. Be more like Feynman - take time to explain things clearly and precisely.
Okay, I'll try, good buddy. Monty Hall is different because it precludes upfront the possibility of there being any ratio other than 1:2. If we were, however, to say that any door could have either a goat or a car, then Monty's elimination of some other door would not inform you on the odds of your door YOUR door. Yea or nay?
The only way for Monty to give you any information at all about whether to switch is if the rule binds him to tell you something about the odds of the unchosen doors. In the original problem, this happens, because the ratio is bound 1:2. In our revised problem, this does not happen - unless he tells you he can't remove a door because neither is a goat. But! Using this as an analogue to our children problem, we've already precluded that possibility upfront by eliminating GG, thus Monty can't provide us any information because his B-G choice is unbound by any rule.
> Why were you running a "computer simulation" of the
> problem? Were you, even?
Moving on ...
>> "The two" ?? What "two"? Your "explanations" are
>> very unclear.
> The only two there are: the two children. The sex
> of one is independent from the sex of the other.
> Monty Hall is different because it precludes upfront
> the possibility of there being any ratio other than
> 1:2. If we were, however, to say that any door could
> have either a goat or a car, then it wouldn't matter
> whether you stayed or switched. Monty's elimination
> of some other door would not inform you on the odds
> of your door YOUR door. Yea or nay?
> The only way for Monty to give you any information at
> all about whether to switch is if the rule binds him
> to tell you something about the odds of the unchosen
> doors.
> In the original problem, this happens, because the
> ratio is bound 1:2.
> In our revised problem, this does not happen - unless
> he tells you he can't remove a door because neither
> is a goat.
> Using this as an analogue to our children problem,
> we've already precluded that possibility upfront
> by eliminating GG, thus Monty can't provide us any
> information because his B-G choice is unbound by
> any rule.
If so, how? Just as Monty's choice gives no information about the door we have selected (and which therefore remains as chance 1/3 of being the winning door), telling us that it's not the case that both children are girls gives us no further information about the other three equally likely possibilities.
So in https://news.ycombinator.com/item?id=7022615 I asked you this ...
A: So now let's take another experiment. I tell
you I'm going to flip two coins until at least
one of them is heads. I do that. Now I ask you
to bet on whether or not there is a tail. What
do you think are fair odds?
B: ...
C: ...
There are three options.
1: Your answers to A, B, and C are not all the same;
2: They are all the same, and not 1/3;
3: They are all the same, and all 1/3.
> The answer to all 3 is 1/2.
I misread A. I agree that it's 1/3 if you flip pairs until at least one is heads. I disagree that living in a world where pairs of tails don't exist and living in a world where pairs of tails do exist but are ignored are the same thing.
>Are you somehow suggesting that the probability distribution of the other options is changed by this?
Yes. I'm saying it's an unwitting double Monty Hall. The fact that he can't give you 3 cars changes the odds. Going (invisibly) from 4 possible worlds (including GG) to 3 changes the prob dist of the remaining 3, by which I mean 2. If Monty must guarantee you at least one boy, then there aren't really 3 remaining possibilities. The unguaranteed can be a boy, or it can be a girl. What is the third?
>> The father says that at least one child is a boy.
>> That eliminates the option of GG. Are you somehow
>> suggesting that the probability distribution of
>> the other options is changed by this?
> Yes. ... Going (invisibly) from 4 possible worlds
> (including GG) to 3 changes the prob dist of the
> remaining 3, by which I mean 2. If Monty must
> guarantee you at least one boy, then there aren't
> really 3 remaining possibilities. The unguaranteed
> can be a boy, or it can be a girl. What is the
> third?
In the Monty Hall case you choose a door, and it has probability 1/3 of being right. It remains 1/3 probable after he chooses a door. The other two doors together have probability 2/3 of concealing the car. It remains 2/3 after he has chosen and opened a door. The probabilities of the branches don't change in any of these cases.
Before you are told anything about the children we have four equally likely possibilities: BB, BG, GB, GG. After one is eliminated, why should the others still not be equi-probable?
> A: So now let's take another experiment.
> I tell you I'm going to flip two coins
> until at least one of them is heads. I
> do that. Now I ask you to bet on whether
> or not there is a tail. What do you
> think are fair odds?
> I misread A. I agree that it's 1/3 if you
> flip pairs until at least one is heads.
> B: Now I hunt among couples with two children
> until I find one that doesn't have two girls,
> and I ask: what are the odds they have two
> boys?
Again, thanks. I apologize.
I'm pleased we got to the heart of it. I remember many times being in a similar situation as yours and I owe much to those too numerous to mention here who were patient with me. All I would say now is that in the future when you find yourself in disagreement, ask if you can learn something, don't just assume you are right. I found that easy, because I had more determination than talent, and was wrong often enough to be reminded constantly that there was still much to learn.
Because in Monty Hall, the effect of changing probability is produced not just via elimination but via process of elimination - which is produced only because sufficient dependencies exist for it: a) the guaranteed 1:2 ratio, b) Monty must eliminate a goat, and c) the goat he eliminates can't be behind your door. These dependencies don't exist in the children problem. Unless Monty's choice occurs under the constraint of avoiding the door we chose, nothing changes. Monty: "You door has a goat behind it" -- so what? Now both of the other doors are 50/50. No similar conflict exists in the other problem. No conflict at all exists in the other problem. Elimination occurs, but it doesn't allow you to do anything further. "No GG" is just one rule, and if one elimination rule isn't sufficient for Monty Hall probabilities to change, why here?
And elimination of what? The elimination not of a possibility, but of a probability? Does that statement even have rational meaning? I'm being dead serious - we can give it mathematical meaning quite easily, but does it even have meaning to begin with?
Yes, I apparently misread that one too. But again, I disagree on the issue of whether the form of the proposed analogue matches the original problem.
>> OK. Now B:
>> > B: Now I hunt among couples with two children
>> > until I find one that doesn't have two girls,
>> > and I ask: what are the odds they have two
>> > boys?
>> Do you agree that it's 1/3?
> Yes, I apparently misread that one too.
>> > C: I hunt among couples with two children until
>> > I find one that has at least one boy, and I
>> > ask: what are the odds they have two boys?
Let's assume for fun that you do agree with that. The original problem was:
A: I met a man who said that he has two children,
at least one of which is a boy. What is the
probability that both children are boys?
B: Among all the couples who have exactly two
children, and such that at least one of their
children is a boy, what is the probability
that both are boys?
> But again, I disagree on the issue of whether
> the form of the proposed analogue matches the
> original problem.
I've made it very clear exactly what my model is for problem B. If you claim that problem A is different, then you need to provide me with a very clear model for your interpretation.
Posturing does not make your arguments more convicing.
> In GB and BG, he has only one way of telling you which is the boy. In BB, he has two. Thus, four possibilities a) GB, b) BG, c) BB and he gave you the first, d) BB and he gave you the second.
How is "ways of telling" you possibly relevant to the puzzle?
You're still apparently committing the same basic fallacy of ennumerating possibilities without assigning them probabilities and basing your argument on the wrong assumption that they must be equally probable.
> Your brain will of course refuse to process the above due to your earlier remark and the sweet, sweet motherfucking irony it would mean.
That describes exactly your behaviour in every single comment here.
With respect to only the sentence above, why is the following table incorrect?
BG 1/3 GB 1/3 BB 1/6 BB 1/6