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 good example of how language and mathematical calculations can be twisted to provide you with whatever answers you want.
There are four possibilities for those children: BB, GG, BG, GB (B for boy and G for girl respectively). So if you say that one of them is a girl, you’ve eliminated the BB point, and you have a 1/3 chance that both children are girls. That’s pretty simple.
But that is only true if you cared about the ordering of the children in the first place.
The second part is just, pardon my language, stupid. First a little aside. The probability we talk about doesn’t actually describe reality, it just describes how certain we are about things. Saying a name won’t suddenly change the child from a boy to a girl, even if the probability suddenly jumped to hundred percent (look up the bayesian calculation of the likelihood that the sun will rise tomorrow if you want another fun mind twister).
But more importantly, giving the girl a name doesn’t give you any relevant information. Julie could still be either the girl in the BG pair, or the GB pair, or one of the girls in the GG pair. However, if you said “I have two children, and the older one is a girl”, that does give you relevant information. The only valid pairs are now GB and GG, so the probability that they have two girls is 1/2. In fact, this would work with any ordering, such as taller/shorter.
It’s like if I said I have a six sided die, and asked you what the probability of rolling a six would be, you’d say 1/6. If I then said “ok, but one of the faces is red”, how would that change the probability? It wouldn’t, it’s not relevant. But if I said, “actually, two of the faces show six”, well that’s different, the probability of rolling six is now 2/6.
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