Brain teaser

"You find yourself sitting next to a stranger on a plane. The following dialogue occurs:

You: 'How many children do you have?'
She: 'Two.'
You:'Is at least one of them a boy?'
She: 'Yes.'

What is the probality that both are boys?"
- Martin Gardner, quoting himself in Weird Water & Fuzzy Logic*

To see the answer, scroll and highlight the hidden text at the bottom of this post (or select highlight all.)

*Gotta love a library book sale. I got a "used" hardcover copy of this for a dollar. I put quotes around used because although the book is wrapped and marked like a library book it's in mint condition and even has that new book smell ... I doubt it was ever checked out.

The intuitive answer is 50%. That's wrong though. Think of it like this:

The woman has two kids ... call them K1 and K2. According to her answers, there are the following possibilities that fit:

K1 - male, K2 - male
K1 -male, K2 - female
K1 - female, K2 male

This means there is a 1 in 3 chance that both are boys - the answer is thus 33%.