> 4) This extra information changes your probability estimate because the possibility of two boys has been ruled out; the naive 1/4 estimate is refined to 1/3.

That’s not correct in general.

It’s only correct if you assume that “3) Someone tells you that the family you drew has at least one girl.” was equally likely to happen whether or not there were two girls.

That’s a quite strong assumption.

One can make different assumptions and get answers different from 1/3. For example, 1/2.

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AIPedant 4 days ago | parent [-]

Unlike the other misreading, I think you are splitting hairs about something boring and irritating. Rephrase the problem instead to "you have a reliable device that can tell whether the family has at least one daughter but doesn't tell you how many."

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kgwgk 3 days ago | parent [-]

> boring and irritating

Ok, AIPedant.

I understand that you may find irritating that someone points out that the original problem is ill-posed and “the answer” depends on how we decide to “rephrase” it.

However, it doesn’t seem boring in the context of a discussion of how the problem is not well-posed and additional assumptions are required to get an answer.

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