In reading the wikipedia article about this subject: https://en.wikipedia.org/wiki/Boy_or_Girl_paradox#Second_question
I understand how the selection process is important in the ambiguous nature of this problem. But i don't exactly understand this part of the "process":
" From all families with two children, one child is selected at random, and the sex of that child is specified to be a boy. This would yield an answer of $1/2$...."
What did they mean by this process cause it doesn't seem to make sense, how can one specify the gender of a random child choosen from the the assortment of families(specify as a boy). Because if i select a girl doesn't that mean that i have a girl? (I understand its a way to get at least one boy though haha)
"For example, if you see the children in the garden, you may see a boy. The other child may be hidden behind a tree. In this case, the statement is equivalent to the second (the child that you can see is a boy). The first statement does not match as one case is one boy, one girl. Then the girl may be visible. (The first statement says that it can be either.)"
First statement does not match, just confused about how the statements are related to this paragraph above?
The following is just the rest of the part of the article.
"While it is certainly true that every possible Mr. Smith has at least one boy (i.e., the condition is necessary) it is not clear that every Mr. Smith with at least one boy is intended. That is, the problem statement does not say that having a boy is a sufficient condition for Mr. Smith to be identified as having a boy this way.
Commenting on Gardner's version of the problem, Bar-Hillel and Falk[4] note that "Mr. Smith, unlike the reader, is presumably aware of the sex of both of his children when making this statement", i.e. that 'I have two children and at least one of them is a boy.' If it is further assumed that Mr Smith would report this fact if it were true then the correct answer is $1/3$ as Gardner intended."
If anyone has a better online resource for this problem do post :)! I am most likely reading this article wrong but it can't seem to get "unstuck" :(.