Probability Can Bite

Re:Probability Can Bite by HWR_14 on Wednesday August 23, 2023 @10:50PM (#37244492)

I think at this point we agree on the math and disagree on how the original question should be read. You saw an implicit alternative to the statement as "I have two children, at least one is a girl" and assumed in the question the parent was saying exactly one of that or the original statement "I have two children, at least one is a boy", possibly chosen randomly, from among the true answers. I read it as a simple statement true statement with GG just being an undefined state for the statement generation, maybe resulting in nothing being said. We could argue about parsing English, but it seems less interesting which question was being posed if we agree on the math behind each parsing, which I think we do?

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Re:Probability Can Bite by kgwgk on Thursday August 24, 2023 @02:19AM (#37245616)

> You saw an implicit alternative to the statement as "I have two children, at least one is a girl" and assumed in the question the parent was saying exactly one of that or the original statement

I made the alternative explicit when I asked you what do you think that the probability is for two girls under the alternative.

And you said 2/3.

> I read it as a simple statement true statement with GG just being an undefined state for the statement generation, maybe resulting in nothing being said.

And with BG and GB being states that generate the statement "I have two children, at least one is a boy".

But then BG and GB cannot generate the statement "I have two children, at least one is a girl".

As a I said there are also ways to justify that the answer to both is 2/3 but they are quite convoluted.

> We could argue about parsing English, but it seems less interesting which question was being posed if we agree on the math behind each parsing, which I think we do?

Maybe we could agree that this is an undefined situation because the answer depends on how you decide to interpret the question?

More precisely, it depends on your assumptions about the (relative) value of P(you tell me that you have at least one boy|you have two boys) and P(you tell me that you have at least one boy|you have one boy and one girl).

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