Can someone explain the Boy Girl Paradox to me?

1.07K 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

For the scenario “I have 2 kids, at least one of which is a girl, whose name is Julie”, start again with the basic possibilities:

Boy/Boy. Boy/Girl. Girl/Boy. Girl/Girl.

Now, *the parent knows* which of the children (the older or the younger) is Julie. Let’s say that Julie is the younger child.

So now the possibilities become:

Boy/Boy. Boy/Julie. Girl/Boy. Girl/Julie.

There are only two possibilities in which Julie is the younger child, and of those possibilities the chance of both children being girls is 1 in 2, or 50%.

We could also have assumed that Julie is the older child, and the result is the same.

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