You can't give a correct answer to an incomplete question. Sit down and define the problem and if you come up with a different answer it's because you made a different assumption about the definition of the observed random variable.
Let's suppose there are four universes.
* Two boys (25% chance)
* Two girls (25% chance)
* Boy and girl (50% chance)
If we assume that the observed random variable has a preimage that contains all possibilities where the statement is true, then we come to the 1/3 conclusion, which is counterintuitive but true. This is the position of the article. I have come to the same conclusion without using order, but I have used the same definition of the observed random variable.
Tell me what you think the random variable is.
We could assume that the random variable has a preimage which only contains the case where both children are boys. Bam, probability 100%, not 1/2 or 1/3. Or we can assome that the random variable has a preimage which only contains the case where one child is of each gender. Bam. Probability 0%. So any answer between 0% and 100% is defensible.
God, I knew this was coming. Since you won't accept my strategy of building up to the complete question (because it is in fact your formulation which is incomplete, and thus I, like you, will not respond to it), let me try this instead:
You misunderstand Monty Hall. I would know; I learned about it by being asked the question and getting it right, not by reading someone else's explanation (which leaves room for misinterpretation). The key to Monty Hall is none of what you stated (or rather, rhetorically asked); it's that the host must pick a door that is both a) bad and b) not yours. If your door is good, then he can leave either, but if your door is bad, then he must leave the good one. So, two possibilities: the door he left was either bad or good, BUT the rule driving his choice wasn't 50/50, so the odds of it being bad or good aren't 50/50, so neither are the odds of yours, even though there are only two left. Take a minute, think about it.
Now ask yourself which "door" (read child) the father told you was a boy. There's the gotcha. Under your/the author's formulation of the question, he doesn't remove a door in the BB universe, but he does in the BG universe. There are two BG's because the table acknowledges that he can tell you which of the two is definitely a boy, and thus he has two options for doing so BUT HE DOESN'T, HE HAS ONE BUT THERE ARE TWO BG UNIVERSES, SO IT LOOKS LIKE TWO.
As mentioned in other replies, it's clear now that you are interpreting the question in a manner other than the usual interpretation, and then being incredibly rude about anyone who disagrees with you.
I have in my hand a device that lets me call up on demand most of the knowledge of the world, and I use it to look at pictures of cats, and to argue with strangers.
> Since you won't accept my strategy of building up to the complete question (because it is in fact your formulation which is incomplete, and thus I, like you, will not respond to it),
No, his formulation is complete and inevitably leads to the correct answer 1/3. You are constantly avoiding a complete formulation of the problem by diverting to a muddled discussion of an entirely different problem. This is NOT about Monty Hall.
Or you're trolling. In which case you are doing it masterfully.
You can't give a correct answer to an incomplete question. Sit down and define the problem and if you come up with a different answer it's because you made a different assumption about the definition of the observed random variable.
Let's suppose there are four universes.
* Two boys (25% chance)
* Two girls (25% chance)
* Boy and girl (50% chance)
If we assume that the observed random variable has a preimage that contains all possibilities where the statement is true, then we come to the 1/3 conclusion, which is counterintuitive but true. This is the position of the article. I have come to the same conclusion without using order, but I have used the same definition of the observed random variable.
Tell me what you think the random variable is.
We could assume that the random variable has a preimage which only contains the case where both children are boys. Bam, probability 100%, not 1/2 or 1/3. Or we can assome that the random variable has a preimage which only contains the case where one child is of each gender. Bam. Probability 0%. So any answer between 0% and 100% is defensible.