Maths problems (interesting ones)

[Kris Verdeyen]

Originally Posted by Denman

ok ok enough debate
the answer is 1/3

Right, 4 possiblities, as most of you got

boy/girl
girl/boy
boy/boy
girl/girl
from genetics
but if you find its a girl, you only eliminate one of them (boy/boy) not 2.
thus the probability - 1/3 (2 where the other is a boy and 1 where other is a girl) .

i quote an answer someone else wrote
You know that they have two children, that is four possibilities (Boy-Boy, Girl-Boy, Boy-Girl and Girl-Girl). Because you know that one of them is a girl, the first possibility is ruled out. So the probability that the second one is a girl is 1/3.

Originally Posted by FizMan

If you want to keep your method of reasoning, we have to add more possibilities. That is, the order of children. I'll mention the first born child, the other is safely assumed to be the second born:


Door Opener / Non Door opener

Boy (1st born) / Girl
Boy (1st born)/ Boy

Boy / Girl (1st born)
Boy / Boy (1st born)

Girl (1st born)/ Girl
Girl (1st born)/ Boy

Girl / Girl (1st born)
Girl / Boy (1st born)


Eliminate the Boys answering the door, you're left with the last four. We can eliminate one of the extraneous Girl/Girl possibilities as well.

Girl (1st born)/ Boy

Girl / Girl (1st born)
Girl / Boy (1st born)

Voila, 1/3.

I understand that the answers you've looked up or been given in finite math class are what you've demonstrated so far. And I understand your answer, and see why it works. What I don't see is why mine was wrong. Your proof above was a bunch of arbitrary hand waving. Why do we need to "eliminate one of the extraneous Girl/Girl possibilites as well" ? If you don't eliminate that - the probability is (surprise surprise) 1/2.

Think for yourselves and come up with the answer! Don't tell me that your high school math teacher told you this was the answer, and therefore it's so. There is more than one way to look at any problem - the challenge here is to determine, at a fundamental level, what is different between the way your math teacher looks at the problem and the way I've outlined it above. I don't see anything fundamentally different, but just because I don't doesn't mean it isn't there.

My proof and Joe's simulation both show the answer to be 1/2. I've also included an Excel simulation that does the same - why are we wrong?