Question: 2014 Winter Final - 21

When a couple has a child, this child is a boy with probability 1/2 and a girl with probability 1/2, independent of the gender of previous children. A couple stops having children as soon as they have 2 girls or 2 boys. Define the random variables

• G = the number of girls the couple has

and

• B = the number of boys the couple has.

Are $G$ and $B$ independent random variables?