The Irksome Tuesday Boy Problem

I suspect you've missed the point. When the answer is clearly 1/3 when the problem is this:

    Take a room full of people.  Ask them all to stand up.
    Then:

        Sit down if you don't have exactly two children.
        Sit down if neither child is a boy.
        What proportion of the remainder have two boys.

The problem is: what made the speaker say that in the first place? Under different assumptions you get different answers. This is akin to the problem:

    Take a stick and break it at random into three pieces.
    What is the probability the pieces can be used to make
        a triangle?

Different people have different interpretations of what it means to say "at random."

Foshee's Tuesday-Boy question helps us see why this is an issue.

    I have a child.  One is a boy, born on a Tuesday.
    What is the probability the other is also a boy?

Using the "obvious" reasoning the answer is 13/27.

    I have a child.  One is a boy, born on a Tuesday, plays the
    piano, juggles, has red hair, and is left-handed.  What is the
    probability the other is also a boy?

Now the same reasoning as gave the answer 1/3 for the first version here gives the answer 1/2 - epsilon. To many this seems wrong, and highlights the importance of being explicit about the assumptions being made.

That's the point of the post, not the naive calculation.

See also Tanya Khovanova's post: http://blog.tanyakhovanova.com/?p=221

There's also a follow-up using Shannon entropy to help: http://blog.tanyakhovanova.com/?p=254