Figuring out the maths for the probability of two adopted teens randomly being matched as pen pals in 2003
Say you're a math nerd and someone poses the question randomly. How would you actually go about figuring it out? If one teen is in the US and the other is in Ireland. What does that look like? How accurate could you get? Is there enough data for a reasonable response?

This question is very vague. It is difficult to provide a mathematically sound answer to this question.

One would need tons of assumptions to give a numerical answer. After some point, too many assumptions in a model are just selfserving.

Okay, apologies, this is my first post. How would I make it more specific? In this situation, both of the teens were adopted and surprised to find this out which is why one of them posed what are the odds of them meeting. Imagine it were a conversation you were having with a new acquaintance, would it be possible to work the math out? How would you go about doing it?

Are you asking for the probability of two wins being penpals given that they were separately adopted, or the probability that two orphan twins get adopted and also end up becoming pen pals?

Separately adopted, one in the US the other in Ireland. They were randomly paired/met as pen pals and had no prior relationship.

I think I can give a reasonable answer to this question, but I have to dig for data and write quite a lot of stuff, to justify the assumptions and get rid of some bias. It's too much work for a 10$ question. For the current amount, I can maybe provide a sketch.

How much is still an assumption? Please forgive me. I am not trying to be obtuse I am willing to talk this out so there is less assumption and more accurate data. Also, what would a more reasonable bounty be?

Well, it depends on the data I can find, but anyway the problem is that the question is not wellposed imo. Assuming the spirit is "I met this person and hey, we're both adopted, what a coincidence!" I can try to do the math, explain why it's not that strange, and go through a few related paradoxes. Regarding the bounty, I'd say somewhere between 20$ and 40$, depending on the level of detail that you want.

If you can provide data about the adoptions/births ratio in the two countries in 2003, that would result in a more accurate answer, and save me some time I can spend to get more into detail instead.

I'm working on the bounty. US info was super easy https://www.johnstonsarchive.net/policy/adoptionstats.html Ireland is a bit muddier.

Bounty increased. Thank you for the input.
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 $20.00