

The Tuesday Boy Problem illustrated with pictures - raldi
http://mikeschiraldi.blogspot.com/2011/11/tuesday-boy-problem-in-under-300-words.html

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wccrawford
I disagree that the Tuesday bit means anything, since the question doesn't ask
about the day of the week. They're saying you can change the odds simply by
giving ANY information, but that's not true. Only information that is
reflected in the question is relevant.

In case that isn't enough, they've counted 2 boys twice 7 times, not just
once. It doesn't matter which is older, as we already established in the
original non-Tuesday question. But in the Tuesday question, they suddenly
though it was different whether the younger or older son was born on Tuesday.
The question doesn't ask about that.

At any rate, it's a bunch of hand-waving and deliberately confusing words. The
chance that any child is male is 50%. (In reality it's not, but whatever.)
Knowing another child's sex doesn't change that. Let's de-confuse it a bit:

The younger child is male. The older child could be male or female.

The older child is male. The younger child could be male or female.

See how nicely that lines up? 50%.

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raldi
Let me phrase it as carefully and unambiguously as I can:

Given that a man has two children and at least one of them is a boy, what is
the probability that the other one is also a boy?

Do you agree or disagree that the answer is 1/3?

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wccrawford
I thought I was pretty clear, and even wrote it out. The chances are 50%.

I disagree with the answer of 1/3.

Here it is again:

If the younger child is a boy, the older child can be a boy or girl. 50%.

If the older child is a boy, the younger child can be a boy or girl. 50%.

If both children are exactly the same age, the other child can be a girl or a
boy. 50%.

Age has absolutely no bearing on sex.

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raldi
Okay, we're making progress here in figuring out where our thought processes
differ. I have two more questions for you:

Imagine a stadium with 1000 fathers, each of whom has two children. (It's some
kind of convention, I guess.) You say, "Everyone who does not have at least
one son, please leave the room." You would expect 750 fathers to remain in the
room, correct?

Now, assuming you answered yes to that question: Imagine you ask these
remaining 750 fathers, "If you have two sons, please raise your hand." Would
you not expect 250 of them, or 1/3, to have their hands raised?

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wccrawford
Yes, 750 would remain. (Assuming 50% of kids are boys, and averages actually
working out, etc etc.)

And yes, I would expect 1/3 of the remaining people to raise their hands, so
250.

The original problem does not go through this process, though. It didn't sort
through a bunch of people to find some that match, and then start asking
questions. It started with group, and some known information about them, and
then started asking questions.

