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
Top answers are pretty accurate. I will try to explain why we wrongly think the answer is 50%.
Intuitively, upon reading the statement, your brain goes “great, so the first one is a girl and the second is either a boy or a girl, so it’s 50/50”. We don’t consider that the girl can be “the second one”.
To everyone saying 33%… Replace the first child with a cat.
I have a cat and a child. What’s the probability my child is a girl?
The answer is 50%. The fact that there is another girl is wholly irrelevant.
PSA: If you read the comments and this still makes no sense, is ebcause OP wrote the phrasing of the paradox wrong and that’s why the paradox makes no sense.
This isn’t about actual probaility (which would be 50% of being a girl).
This is about ambiguos phrasing that allows assumptions that enable these “paradoxes”. As OP phrased it wrong, specially the second and third scenario don’t make sense. People are repying with the answers to the actual paradox, which uses a different phrasing than the OP wrote.
Lots of wrong answers in this thread. Naming the child doesn’t change the probability. The original and correct version of the puzzle says that “my oldest child is named Julie”. This does change the probability because you fix the oldest child being a girl. It’s not the name that matters but the fact that in the BB, BG, GB, GG scenario now we have fixed that it starts with a G.
I think there are good answers here, but I want to point out for anyone curious or in the know, that this is a slight variation on the “Monty Hall Problem”
It’s cool for me because I never witnessed it from this angle.
I conceptualize it as a grid with 4 boxes: BB, BG, GB, GG
Those are all 4 combinations of having 2 kids. Well, obviously it can’t be BB because we know there’s at least one girl
What is left after you remove BB:
BG, GB, GG
Two of those possibilities have a boy as the second child. 2/3
One of those possibilities has a girl as the second child 1/3
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