An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem.
Let's make up a hypothetical, though not unrealistic story.
First we need the empirical frequency of a birth giving twin boys, which turns out to be about 5/1000. Second, amongst 2-child families in general, the frequency of "2 boys" must be about 1/4. So we can estimate the population ratio
(number of families with twin boys, no other children)/ (number of families with two boys, no other children) = approx 2%.
(Note the
"interesting" implicit assumption here is that having twins rather than non-twins
doesn't affect the frequency of having additional children).
So we interpret ratio of frequencies as a conditional probability
P(twins | 2 boys, no other children) = approx 2%
and then give "about 2%" as the answer to the original question.
Analysis. This answer is drastically wrong. The information we have is not "2 boys, no other children" but instead the information is the specific form of the response "yes, two boys". A person with twins might well have mentioned this fact in their response -- e.g. "yes, twin boys". And a person with non-twins might have answered in a way that implied non-twins, e.g. "Sam's in College and Jim's in High School". Perhaps the best answer to the original question is
2% times p/q; where
p is chance a person with twins answers in such a way that you can't infer twins
q is chance a person with non-twins answers in such a way that you can't infer
non-twins.
Common experience is that people with twins would actually tell you, so let me guess
$p = 1/8$ and $ q =1/2$, leading to my answer "0.5%", which I would bet a small
amount of money on.
Commentary. The abstract point is that, for doing probability calculations
Rohit Parikh comments: in analytic philosophy, this is an implicature: "something meant, implied, or suggested distinct from what is said".