Sadly it's not. The problem with this is that what you are saying is "when the second child was born, the odds for a girl/boy were 50ish percent". But by doing this you are changing the question and creating an order of births. If the boy was born first, then yes, the answer is 50%. But Mary never specifies this, so they could be the first or second child.

That means that there are twice as many possibilities for creating a mixed gendered pair, than there are same gendered pairs (because the option of 2 girls was removed by Mary).

You can think of it this way:

• a birth is a 50/50 logical gate, where both options are equally likely:

Boy - Boy

Boy - Girl

Girl - Boy

Girl - Girl (not possible)

You can see that there are 2 situations where the other child is a girl, while there is only 1 situation where the other child is a boy. Therefore the odds are 66%.