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?

---

Possibly related posts: (automatically generated)

• Boy Pageant Contestants Gaining Visibility
• Wanting a boy, getting a girl
• Jury selection to begin in trial of Texas sect member