Can someone explain the Boy Girl Paradox to me?

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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

How is everyone in this thread so wrong? The answer to the first question is 50%, not 33%. This is not a paradox in any way. The probability of the sex of one kid is entirely independent on the sex of another. A family could have 99 girls and the probability of the 100th kid being a girl is still 50%.

Everyone here seems to be breaking this up into possible family combinations, yet they overlook two of the possibilities involving the boy/boy and girl/girl combinations. So there’s B/G, G/B, B/b, b/B, G/g, and g/G. Since one is a girl, elimination the two boy combinations and we’re left with: B/G, G/B, G/g, and g/G. There’s 2/4 combinations with a second girl. The answer is 50%.

Everyone claiming otherwise is wrong. Flat out. ORDER DOES NOT MATTER

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