I like numbers after all

I remember when I was in highschool. One of the most dreadful of all test questions was always the word problem, especially in math. Do you remember those? The ones that always started off with two trains travelling toward each other at high speed, which never really made sense to me at all, since if it were true, they would both hit the brakes sooner or later.
But somehow, now that I am way old, I really kind of like them. Or at least the good ones.
There is a difference between the good ones and the bad ones. The bad ones have to do with counting the apples or figuring out how much older John is. But the good ones are different.
The good ones make you think along lines that you didn't consider at first. I'll give you an example. This one is The Classic.

Imagine you were in a stadium full of people and had everyone who had two children come foreward. Then you asked those people to raise their hand if they had at least one boy.
At that point, everyone who didn't raise their hand (those who had two girls) could go sit back down. Now out of all of those people remaining (those with two children, at least one of which was a boy) what percentage of them should have two boys?

Did you say fifty percent? If you did, you are among the oogles of people who missed that one.
I know what your logic is. You reason that if one is a boy, the other is either a boy or a girl, and since you have a fifty-fifty chance, the odds are fifty percent. Makes perfect sense. However, it is wrong.

No, it is not a trick question. The real answer is 33 1/3%.
But how is that possible?
Take another look at the question and see if you can figure it. I promise you, it's true.

The key is in how it is set up. Here's how it works:

If you got married and had two children, there are several possibilities.
1. you could have two boys.
2. you could have a boy and a girl.
3. you could have a girl and a boy.
4. you could have two girls.
So if you take away those with two girls, you have three choices remaining, with even odds for each, so one third of them should have two boys.
Now I guess you could throw in fraternal twins and skewer the odds somehow, but that's not the purpose here.

What's good about that one is that you have to stop and think about it more deeply than it appears at first.
That's one of the really easy ones, but it's quick to write, so that's why I picked it.

I'll see if I can put down a harder one next time. But usually, you are not supposed to tell the answer. Ever. The really hard ones can take days to figure out, so be warned.