at least one is a boy

# from http://jsteinhardt.wordpress.com/2010/09/13/nobody-understands-probability/

<quote>
Let’s consider an example. Suppose that a man comes up to you and says 
“I have two children. At least one of them is a boy.” 
What is the probability that they are both boys?
</quote>

Note: we are assuming the man is telling the truth.  
Justification: Any probabilistic analysis presumes that given facts are true.

Given that a man has two children, there are 4 possible gender configurations:
1. GG
2. GB
3. BG
4. BB

We know that each configuration has an equal probability since:
* any individual birth has equal gender assignment probabilities
* any given gender assignment is independent of previous gender assignments.

Note that we are *not* answering the question: what is my next-born child's gender?

Since at least one is a boy, we can eliminate configuration #1, leaving 3 options that satisfy this condition:
2. GB
3. BG
4. BB

What is the probability that both are boys?
1/3, since only configuration #4 satisfies this condition.