The Paradox of the Children

Suppose you meet a mathematician in the street. Around here that is not such a far fetched thing.

And it comes to pass that she mentions that she has two children.

"Are either of the children boys?" you ask.

Yes, she says, with a cryptic smile, and speaks no further word.

And later, you meet another friend, who is a betting man. And you tell him your story.

He says "I bet you £50 that the other child is a boy."

Should you take the bet?


Consider: Had you asked "Is the older child a boy?", then the bet would be fair.
And had you asked "Is the younger child a boy?", then it would be fair.

And the boy must be either the older or the younger.

Related: How likely is the king to have a sister?