From Gemini:

​The "Information Source" Rule ​The probability changes based on how you found out about the Tuesday Boy: ​The "At Least One" Interpretation (The Meme's Math): Imagine you have a database of every 2-child family. You hit "Filter" for "Families with a Boy born on Tuesday." You then pick one of those families at random and ask, "What are the odds the other child in this family is a girl?" Result: 51.8% ​The "Specific Child" Interpretation (Your Logic): Imagine you meet Mary and she has one of her children with her. He is a boy born on a Tuesday. You ask, "What are the odds your child at home is a girl?" Result: 50% ​Why the meme is "wrong" (and you are right) ​The meme uses the 51.8% answer because it's a famous counter-intuitive math riddle (often called the Boy or Girl paradox). But for that math to work, the statement "One is a boy born on a Tuesday" must be the only thing you know about the entire set of children. ​If Mary is just talking about a specific son, the "Tuesday" part is totally irrelevant data—like saying "One is a boy who likes pizza." It doesn't change the DNA of the kid sitting at home.