Hmmm I think we're saying more or less the same thing. The point I wanted to make is that
"I have a son and a daughter"
is the same as
"I have a daughter and a son"
unless you qualify the statement with further information - names (Alex and Sam from your post) would be an example of that further information. My feeling was that ars is implicitly 'filled in the blanks' somewhere, treating the two children as distinct when in fact they have to be interchangeable for the purposes of the original (13/27) calculation.
It's the lack (or not) of such details that alters how the probability is calculated.
I admit though that I'm still chasing myself in circles trying to understand the whole thing so take this reply with a pinch of salt ;-)
"I have a son and a daughter"
is the same as
"I have a daughter and a son"
unless you qualify the statement with further information - names (Alex and Sam from your post) would be an example of that further information. My feeling was that ars is implicitly 'filled in the blanks' somewhere, treating the two children as distinct when in fact they have to be interchangeable for the purposes of the original (13/27) calculation.
It's the lack (or not) of such details that alters how the probability is calculated.
I admit though that I'm still chasing myself in circles trying to understand the whole thing so take this reply with a pinch of salt ;-)