Can someone explain the Boy Girl Paradox to me?

1.08K views

It’s so counter-intuitive my head is going to explode.

Here’s the paradox for the uninitiated:If I say, “I have 2 kids, at least one of which is a girl.” What is the probability that my other kid is a girl? The answer is 33.33%.

>*Intuitively, most of us would think the answer is 50%. But it isn’t. I implore you to read more about the problem.*

Then, if I say, “I have 2 kids, at least one of which is a girl, whose name is Julie.” What is the probability that my other kid is a girl? The answer is 50%.

>*The bewildering thing is the elephant in the room. Obviously. How does giving her a name change the probability?*
>
>*Apparently, if I said, “I have 2 kids, at least one of which is a girl, whose name is …” The probability that the other kid is a girl* ***IS STILL 33.33%.*** *Until the name is uttered, the probability remains 33.33%. Mind-boggling.*

And now, if I say, “I have 2 kids, at least one of which is a girl, who was born on Tuesday.” What is the probability that my other kid is a girl? The answer is 13/27.

>*I give up.*

Can someone explain this brain-melting paradox to me, please?

In: 4

26 Answers

Anonymous 0 Comments

Here are all the possible combinations of Boy and Girl for your two children:

* BB

* BG

* GB

* GG

Now we know that at least 1 is a girl, so let’s narrow that down to only combinations with at least one girl:

* BG
* GG
* GB

Out of those 3 combinations, 2 end up with the other child being a boy, and 1 with the other child being a girl. So there’s a 1/3 possibility, or 33.3…% that the other child is a girl.

You are viewing 1 out of 26 answers, click here to view all answers.