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» The Ornery American Forum » General Comments » Annoying probability question of the day (Page 7)

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Author Topic: Annoying probability question of the day
Aris Katsaris
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Coolness. I must have missed or forgotten that post.
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Jordan
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I saw that post, but when you followed with:

quote:
Badvok:
But you are just solving the wrong problem and hence using the wrong numbers for the problem. We have ONE father, ONE son, and ONE other child who's gender we do not know.

I interpreted that, combined with your earlier comparison of bad arithmetic, as meaning that you didn't believe the same logic would apply in the case of one father about whom we know only that he has at least one son. Was I wrong? [Smile]
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Badvok
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Oh my, I am such an idiot!

I just couldn't let this go, my brain kept on working on it and so I've reviewed what I've said again. I never once explained why there is only a single unknown - stupid!

Let's review the original statement again:

quote:
John Doe comes up to you and says: "I have two kids. One of them is a boy. He was born on a Tuesday." What are the odds that he has two boys?
All I see is one father, one son and one other child.

Why is there only one other child and hence only a single unknown? The statement 'HE was born on a Tuesday." is not totally irrelevant but identifies one of the two children because of the pronoun used!

If he had said "one is a boy born on Tuesday" that would be different because there is no pronoun and hence no identification of an individual.

The "Tuesday" value itself is irrelevant because the question is only about gender. My understanding in this case can be shown by replacing this bit with "He has light brown hair." - we are now unable to enumerate all the possibilities but does this change the answer to the question of whether both are boys?

Of course this is all about interpreting English language and hence it is always possible to interpret it another way. However that was my interpretation which I failed to previously explain.

Thanks to DonaldD for questioning my inclusion of "It was scratched." in my alternate version - it is not irrelevant it is key to reducing the problem to a single unknown.

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Jordan
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quote:
Badvok:
Why is there only one other child and hence only a single unknown? The statement 'HE was born on a Tuesday." is not totally irrelevant but identifies one of the two children because of the pronoun used!

I'm unimpressed enough by the original phrasing of the question that by now I'm willing to grant anyone's particular interpretation rather than bothering to argue. As I said on the first page it's pretty ambiguous.

So if I gather correctly, you accept that it's 1/3 if you don't know which child is being referred to, but you consider the phrasing of the question to preclude that condition. I suspect you've tamed a few savage breasts with that! [Smile]

Though there's still time to discuss how knowing that at least one is born on a Tuesday affects the probabilities, if you're up for it! [Big Grin]

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Aris Katsaris
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quote:
Why is there only one other child and hence only a single unknown? The statement 'HE was born on a Tuesday." is not totally irrelevant but identifies one of the two children because of the pronoun used!
Completely agreed with this. As the pronoun specifically identifies the child, the odds are at 50%.

If the puzzle was however phrased like this:
Father: I have two children.
Me: Was at least one of them a boy born on a Tuesday?
Father: Yes.
The possibility for two sons would now be 13/27 as elsewhere detailed.

The more specificity about the child in our probing question the more the probability goes from 33% to 50%. For example.
Father: I have two children.
Me: Was at least one of them a boy that is the current Governor of Alabama?
Father: Yes.

This is 50% again since the boy is specifically identified by the fact only one governor of Alabama can exist at a time.

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DonaldD
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Jordan...
quote:
If he had said "one is a boy born on Tuesday" that would be different because there is no pronoun and hence no identification of an individual.

The "Tuesday" value itself is irrelevant because the question is only about gender.

BTW, Badvok
quote:
Thanks to DonaldD for questioning my inclusion of "It was scratched." in my alternate version - it is not irrelevant it is key to reducing the problem to a single unknown.
I don't think I agree with your interpretation of my statement, here. I suggested something being scratched as not equivalent to a child being born on Tuesday not because it identifies the item (it does not necessarily, any more than does a Tuesday birth) but rather because the probability of a scratch is indeterminate.
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Jordan
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Sorry Donald—I can see you're drawing my attention to what Badvok said, but I'm not sure why yet! [Smile] Have I missed something?

Edit: in case it's not clear, I get the impression now that Badvok understands and accepts that there is a 1/3 probability of there being two boys when the question is carefully phrased, but I went with interpreting the second sentence that you bolded as implying that he doesn't yet accept the 13/27 answer to the case of at least one boy born on a Tuesday.

Isn't English fun? [Wink]

[ July 30, 2010, 08:33 AM: Message edited by: Jordan ]

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Jordan
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quote:
Aris Katsaris:
The more specificity about the child in our probing question the more the probability goes from 33% to 50%. For example.
Father: I have two children.
Me: Was at least one of them a boy that is the current Governor of Alabama?
Father: Yes.

This is 50% again since the boy is specifically identified by the fact only one governor of Alabama can exist at a time.

Aside from being the only time I recall seeing the word "specificity" used to refer to anything other than CSS selectors, that's an admirably clear summary of the principle at work, Aris.
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