A simple logic problem

I just need to get this out of my head. Pete sent a few logic problems, but this one kind of confused me.

Walking down the street one day, I met a woman strolling with her daughter.
“What a lovely child,” I remarked. “In fact, I have two children,” she replied.
The question: What is the probability that both of her children are girls?
Be warned: this question is not as trivial as it may look.

Try to think about the answer before reading on. I might also confuse you.

My answers:

Before reading the ‘warning’, the first answer that popped on my head was 1/2. Her sibling is either a boy, or a girl. So, 1/2.

When I read the warning, I thought… “Oh, ok. There are four options. Girl/Girl, Girl/Boy, Boy/Girl and Boy/Boy. Obviously Boy/Boy isn’t possible, so it’s 1 out of 3. So, 1/3.”

Upon further analysis, I thought, “But what is the probability that the mother walked with the first girl vs the second? I should factor in the probability of ‘the mother picking a particular child to walk with her’. So now, I have eight options (x denoting the fact that the mother strolled with that particular child): xBoy/Boy, Boy/xBoy, xGirl/Boy, Girl/xBoy, xBoy/Girl, Boy/xGirl, xGirl/Girl, Girl/xGirl. There are only 4 possible options, since we know the fact that the mom walked with a girl: xGirl/Boy, Boy/xGirl, xGirl/Girl, Girl/xGirl. There are 2 out of 4 chances that her children are both girls. Which brings us back to 1/2.”

I stick with my last answer. The answer is trivial but the solution isn’t as easy as you’d initially think.

Which solution do you think is the correct one? Do you have another solution?

Another deadly storm

I’m sure you’ve heard about (or worse: experienced) the typhoon Durian. I’ve only heard about it on CNN and INQ7; and read about it on the net. I’m not going to describe how awful it was (or at least, how awful I read/heard it was), just google “Typhoon Durian, Philippines” and you’ll see millions of results.
The Bicol region is my parent’s hometown. This was the region that the super typhoon hit the worst. We have a handful of relatives there. We’ve recently found out that one of them was found in the morgue. Two of our relatives were reported to have survived, probably now orphans, but are in grave condition. Quite a few of them are still missing, and I’ve heard that the government is not optimistic in finding the missing people. We have a few more relatives from another city that we’ve heard nothing from. No one has heard from them yet. I really hope they’re fine.
I pray for the survivors, the missing and the souls of those who died in this tragic calamity.