Woman with two children

Did someone change the lock to this forum's door???

Here is one:

Census Taker: How many children do you have?
Woman: Two.
Census Taker: And their ages?
Woman: One is five, one is two.
Census Taker: Is one of them a girl?
Woman: Yes.

What is the probability that her other child is a girl?
(Assume every pregnancy has a 50/50 chance to be a boy or a girl.)

Show your work.

-Ray.

1/3 chance of the other being a girl.

Since we know one is a girl, the combinations could be:

GG, GB, BG.

Good work.

-Ray.

Keeping with your 50/50 assumption, what is the probability that a woman who is pregnant for her second time, and who has previously given birth to a girl, will give birth to another girl?

Please refer to the numerous Monty Hall Problem threads.