Probability Puzzles

There's an intersting discussion of some confusing Probability Puzzles on John Baez's new blog.

“I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?”

The "born on a Tuesday" information can't possibly make a difference, can it? So the answer should be same same as:

“I have two children. One is a boy. What is the probability I have two boys?”

Shoudn't it?

There's a thorough analysis at Some Thoughts on Tuesday's Child by Greg Egan.