Dear Andrzej,

> The uncertainty is in the definition of the sets A and B.

Agreed. Why choose an ambiguous definition? Or: why are you asking for
unique answers to questions which you admit are ambiguous?

> Where is the probability?

If your question is "where does probability theory come in when we are
dealing with ambiguous language?", one can look at a probability
distribution over the possible intended interpretations, if we assume the
"intended interpretation" is what we are interested in (e.g. if we are
writing an exam and want to maximise our mark). Or we can look at a
probability distribution over how a hearer might respond to an ambiguous
question, or whatever. Once you've told us which well-defined question to
analyse, we can use our tools to analyse it.

> Where is randomness?

I still don't see why you are looking for randomness - you don't need 
randomness to apply probability theory.

Konrad

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