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by AIPedant
297 days ago
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I have no idea what point you're trying to make. I am aware the selection process is different. If you understand the argument now but you're just splitting hairs about whether it's similar to Monty Hall, fine let's agree to disagree. If you don't understand the argument and are trying to use the dissimilarity to Monty Hall as a counterargument then I don't think I can help you any further. This is not coherent as written: If I flip a dime and a quarter, and tell you that one of them is heads, do you have increased chance of knowing if either particular one is heads? This is more liar's dice than it is monty hall.
"Increased chance of knowing" is nonsense. What you mean is "increased chance of being correct if I guess the dime came up heads instead of tails" and this is obviously true. Given at least one of the two coins came up as heads, the probability that the dime is heads is 2/3rds, not 1/2. |
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The crux of my view on this problem is that I can make an "at least" or an "at most" statement only knowing what one of the coins is, specifically. So, we both flip a coin, I look at mine and say "at least one is heads." You do not get an increased odds of knowing your coin, obviously. (This is the general play of liar's dice. Just, with dice. :) )
That all said, I largely land on agreeing with one of the other commenters here. The assumptions you can bring to this scenario are rather large here. The assumption I would hold would be to mirror this with how it could happen "in the world." And most ways of selecting a family where "at least 1 is a girl" has you encountering a girl. That is, ordering the two events and revealing one at a time.
In modeling this, you could say that you have two coins, one marked with heads on each side and the other a standard fair coin. In this, I can easily see how your odds of seeing heads on the first coin is increased, but odds on them being both heads is now back to 1/2. I can see how this is not the same modeling you are using, but it is still one that I have a hard time shaking from my intuition on the problem.