Manolis comments on Paul's post summed it up pretty well for me.
What feels counter intuitive is that announcing the gender of one child seems to increase the chances of the other child being of a different gender, but it's actually the opposite.
"Family with 2 children" ->
chance of having at least one boy: 75%
"but I have at least one girl" ->
chance of having at least one boy: 66%
"but the first one is a girl" ->
chance of having at least one boy: 50%
"but they're both girls" ->
chance of having at least one boy: 0%
What feels counter intuitive is that announcing the gender of one child seems to increase the chances of the other child being of a different gender, but it's actually the opposite.
"Family with 2 children" -> chance of having at least one boy: 75% "but I have at least one girl" -> chance of having at least one boy: 66% "but the first one is a girl" -> chance of having at least one boy: 50% "but they're both girls" -> chance of having at least one boy: 0%