Maths problems (interesting ones)

[Kris Verdeyen]

Look at it like this: there are two children, one who opens the door, and one who doesn't. Before she opens the door, the possibilities are:

Door Opener / Non Door opener

Boy / Girl
Boy / Boy

Girl / Girl
Girl / Boy

Once she opens the door, the first two possibilities are eliminated, leaving only the options that the shy child is either a Boy or a girl. In other words, the sex of the one child has nothing to do with the sex of the other.

Prove me wrong.


EDIT:

Even better, look at it like this:

FAMILIES WITH TWO CHILDREN:
25% have two boys - A girl will answer the door 0% of the time
50% have a boy and a girl - A girl will answer 50% of the time
25% have two girls - a girl will answer 100% of the time

If we take the product of the two percentages in each row, we get some more numbers to cloud the issue:

PROBABLILITY THAT A GIRL WILL ANSWER...
...and the family has two boys - 0%
...and there's a boy and a girl - 25%
...and the family has two girls - 25%

So, a girl will answer (0% + 25% + 25%) = 50% of the time.
Exactly half of those responses will come from families with two girls, and exactly half will come from families with a boy and a girl.

Or I could be completely off base - let me know.