Probability of having a Girl A and B are married. They have two kids. One of them is a girl. What is the probability that the other kid is also a girl?
Someone says $\frac{1}{2}$, someone says $\frac{1}{3}$. Which is correct?
Now A and B have 4 children and all of them are boys. B is pregnant. So what is the probability that A and B are gifted with a baby girl?
Is it $\frac{1}{2}$ or there will be some conditional probability?

Originally there are $4$ equiprobable possibilities: BB,GB,GG,BG.
Condition "at least one of them is a girl" leaves open $3$ (again) equiprobable possibilities: GB,GG,BG. 
Draw your conclusion.

Answer in short on second question: independence. 
Again draw your conclusion.
