Why can you not frame it as: "a random family has been sampled, the sample family has two childs, one of them is a girl"?

I.e. without "discarding", just giving some additional, but not complete, information on the random sample. Is adding information about the picked sample the same as discarding all contrarian samples? Why is this relevant?

If there were two possible statements they asked

"a random family has been sampled, the sample family has two childs, one of them is a girl"?

and

"a random family has been sampled, the sample family has two childs, one of them is a boy"?

and they selected each statement based on randomly picking a child from a random family then the probability actually becomes 50% boy/girl for the next child since the boy/boy or girl/girl has twice the chance of generating the above statement for the respective gender compared to the mixed gender children family.

Ie. if they say one is a girl that statement had a 50% chance of being generated by a girl/girl family (since we pick the statement based on a random selection of one of the two childrens gender and there's 2 girls, doubling the chance of a statement that one's a girl coming from a girl/girl family), there's 25% chance the statement was generated from a girl/boy family and a 25% chance the statement was generated from a boy/girl family.

If you take 50% chance girl/girl, 25% chance boy/girl and 25% girl/boy you'll see there's a 50/50 chance of the next child being either gender.

All this due to changing how we sampled.

> a random family has been sampled, the sample family has two childs, one of them is a girl"

It’s not a random family if it must have at least one girl. If you want to talk about a random family you can only make statements of the kind “one of the children is <gender>” where the gender depend on the specific family or “the family has between 0 and 2 girls”

[dead]