Super Duper Extra Hard Brainteaser

[jimdmcevoy]

I'll open with a well know semi-easy one:

You know that a woman has exactly 2 children. You ask her if she has at least one girl, and she says yes. What's the probability that she has two girls?

Answer in white:

<font color="white"> 1/3 </font>

Now, suppose that 1% of all girls are named Sarah, and that if a mother had two girls that the mother would not name both of them Sarah

You know a woman has exactly 2 children, you ask her if she has a girl named Sarah, she says yes.

What are the chances she has two girls?