/sci/ - Science & Math

So my wife and I are having twins. Two weeks ago the doc drew some blood for a screening test that will look at the little bits of fetal dna in her blood and determine if we are having a retard. They also said that they could kind of determine the gender - if they detected XX chromosomes only then we are having two girls. If they detected a Y chromosome then there's at least one boy, but beyond that they couldn't say whether it's boy/girl or boy/boy.
Got the results today. No retards in there. Y chromosome detected. At least one boy. Then the doctor said - 50/50 chance of the other one being a girl.
But that struck me as being possibly wrong. Maybe like that monty hall problem or something like that. Isn't it a 2/3 chance the other is a girl?
Or am I overthinking it?