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
This is a variant of the Monty Hall problem. You have an unknown probability and some information. So, if you just say “I have two children”, there are four options:
* two boys
* older girl, younger boy
* older boy, younger girl
* two girls.
When you add the fact that one is a girl, you have only eliminated the first possibility. However, that fact says nothing about which of the other three possibilities it is. In two of the three cases, the other child is a boy, so what’s left is a 1 in 3 chance that the other child is a girl.
Giving a name or a birthday adds more information. There are 27 possibilities for one child being born on a Tuesday, 13 of which are the pairing of two girls.
[Chart](https://www.jesperjuul.net/ludologist/wp-content/uploads/2010/06/fullGrid.png)
The name is even more unique, as there are a near infinite number of names the children could have. Technically the probability of a second girl is 49.99999…999%, but you can round to 50 because there are only so many people who would name their children the same thing.
*George Foreman has entered the chat*
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