I have two children. One is a girl born on a Thursday.
What is the probability both of my children are girls?
I’ll bite. 50 percent.
This may better belong in the Game Room forum.
Bite again.
Well, let’s see. “Thursday’s child is fair of face”. That’s no help…
It’s not a straight math problem or 50% would be correct…
Perhaps it’s someone famous with 2 kids, one of whom is a girl born on Thursday???
Straight math problem.
Blink. Blink.
2 kids. There is, from the data, a 100% chance one is a girl. This no longer factors into the consideration, as it is a given.
There is a 50% chance the other is a girl.
Ergo, 50%. Straight math.
Straight math. Not 50%. 
Assume an even chance that a random child is born boy or girl and that birth on any day of the week is as likely as any other.
Insufficient information for a meaningful answer.
First, we need to know whether by “one is a girl born on a Thursday”, you mean exactly one, or at least one.
Second, more importantly, and more subtly, we need to know what led to us having that information. Did someone ask you “Is at least one (or exactly one) of your children a girl born on a Thursday”, and you answered yes, or did you pick one of your children at random, and then tell us that chosen child’s birth day and gender? Or some combination: Like, someone asked “Is at least one of your children a girl”, and you answered “yes”, and then (choosing one at random if you have two), you also specified that child’s birth day?
Ok. One being born on a Thursday does not preclude the other being born on a Thursday just like one being a girl does not preclude the other.
I told you this as a statement of fact, no more or less, nothing more specific to either child.
Why do I suspect the correct answer is either 0% or 100%?
Then my assessment stands: We can’t find an answer until we know why you told us this fact.
The most natural process that would lead to you revealing this fact would be the choose-a-child-at-random process, but that one leads to the answer of 50%, which you have already told us is incorrect. So now we’re just trying to figure out what particular unnatural thought process you were using.
I told you this as a riddle, with no indication of which child I mean. There is no unnatural thought process. I am saying, using only the pieces of information available to you, what are the odds I have two girls. The answer is not 50%.
I disagree with your assessment.
Could the other child also be a girl born on a Thursday or no?
In other words, simply assume I have two children and at least one of them is a girl born on a Thursday. Now, knowing only that, the probability that both are girls is…
Further clarification: The other child could have been born on a Thursday.
This is meant to be a simple math probability question, so if you prefer to replace “I have” with “A random person has”, that is OK.
Are you going for “there are 2 possible sexes X 7 days=14 possibilities but it’s not a girl born on Thursday, so remove 1 possibility=>13 possibilities of which 6 are girls and 7 are boys so the probability is 6/13”?
If there are no unnatural thought processes involved, then the mathematical answer is 50%, because the natural way for us to have gotten that information is for you to have picked a child at random and told us that child’s birth day and gender.
But to fully lay it out: You have two children, the one you chose to tell us about and the one you didn’t. The chosen child can have any of seven birth days and any of two genders, or 14 possibilities. We can assume that all birth days and genders are equally likely, and further that birth day is independent of gender, and so all 14 possibilities are equally likely. Similarly, the non-chosen child has 14 possible choices of gender and birth day, and we also assume that those are equiprobable, independent of each other, and independent of the first child. So our initial universe of discourse has 196 equiprobable possibilities.
Then, you tell us that your chosen child is a girl. That rules out 98 possibilities. And then you tell us that your chosen child was born on a Thursday. That rules out a further 84 possibilities. 14 possibilities remain, all pertaining to the non-chosen child’s birth day and gender:
Boy, Sunday
Girl, Sunday
Boy, Monday
Girl, Monday
Boy, Tuesday
Girl, Tuesday
Boy, Wednesday
Girl, Wednesday
Boy, Thursday
Girl, Thursday
Boy, Friday
Girl, Friday
Boy, Saturday
Girl, Saturday
Of those 14 equiprobable possibilities, in 7 the non-chosen child is a girl, and in 7, the non-chosen child is a boy. Thus, 50%.