Saturday, May 10, 2014

Problem

You and a friend are standing in front of two houses. In each house lives a family with two children.
"The family on the left has a boy who loves history, but their other child prefers math," your friend tells you.
"The family on the right has a 7-year old boy, and they just had a new baby," he explains.
"Does either family have a girl?" you ask.
"I'm not sure," your friend says. "But pick the family that you think is more likely to have a girl. If they do have a girl, I'll give you \$100."
Which family should you pick, or does it not matter?

Solution

They offer these charts for the houses:

Left house:
Younger Older
Girl Boy
Boy Girl
Boy Boy

Right house:
Younger Older
Girl Boy
Boy Boy

They also tell us:

"This is a very counter intuitive riddle. It seems like there should always be a 1/2 chance that a given child is a girl. And in fact there is. The key word there is "given". Because we are not asking about a "given" child for the house on the left. We are asking about what could be either child."

And I'll just stop it right there. In the riddle, you ask your friend "Does either family have a girl?", and the friend responds "pick the family that you think is more likely to have a girl."

This, to me, seems to be specifically asking the question "Is or is not the other child a girl?"

When the solution says "We are asking about what could be either child.", they seem to be suggesting that, at some point, they were asking the specific question "Is the other child a younger girl, a younger boy, an older girl, or an older boy?"

The riddle itself, however, was not asking this question; the riddle was asking if, yes or no, the other child was a boy or girl, and that the family had a child that was a girl, regardless of age.

If they were asking "what could be either child", they might as well have added in more factors, such as whether or not the other child could have been a long or short haired, green or brown eyed, taller or shorter, stronger or weaker, younger or older boy or girl.

There are a lot of things the other child could have been, but I don't think any of those other factors have anything to do with what the riddle asks, which is to "pick the family that you think is more likely to have a girl." And age doesn't have anything to do with whether the child is more likely to be a girl, correct?

The solution seems to me to be asking a question that the riddle itself was not.

And this doesn't seem to be an open-ended riddle either, that has a case of "we're both right"; the way this riddle is set up, and with the solution they give, they are saying that there is a single solution to this riddle of which house has a higher probability.

Please correct me if I'm wrong, and point out any flaws on my end. I honestly believe their solution is incorrect, or they changed around the original question to something that it actually wasn't. Something just doesn't seem right here. :/