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This is why conditional probabilities are fun.
The first question is interesting because it isn't what it seems. It refers to something that has ostensibly already happened and so it requires one to map out all the different ways that such a thing could have happened. If it were posed differently, say, "If you know a family already has one daughter, what are the odds that their next child will be a girl?" you'd get the expected 50%.
There is a subtle distinction between what has happened compared with how it could have happened and what could happen compared with how it could happen.
So if you decide that birth order isn't important, then you do get 50% for both examples.
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