I see a white poodle. Does it increase the probability that all crows are black?

Question

I have this question in my home assignment I haven't been able to solve it. There is no further context to this question, only "I see a white poodle. Does it increase the probability that all crows are black?".

So far, I have two possible answers/theories.

1. If there are finitely many colors and finitely many animals/humans/whatever that have a color, I feel like if one animal (poodle in this case) occupies this one 'slot' for white color, it should mean that the number of all possible color combinations decreases for the whole population of crows - therefore 'yes' indeed, the probability of all-black crow population increases.

2. A white poodle being born cannot logically in any way influence the color of a crow. So the answer would be 'no'.

These two theories are obviously contradictory, so my question is - which one is correct? Or have I made a mistake and neither one of them is correct?

Thank you so much for help. E.

Answer 1

User degenerated_matter wrote: "The question is probing your understanding of the independence of statistical events". In this sense, note that your intuitive explanation for the unintuitive answer (your notion of slots, that is) is exactly wrong.

The paradox does not stem from there being only finitely many 'slots' but from the logical equivalence of the two statements 'All A are B' and 'C not being B makes C not being A', both of which can be backed by evidence that look unrelated.

To conclude: accept that neither and both answers are correct, for it truly is a paradox.

Answer 2

You could argue the answer is "No" on the grounds that the meaning of "white" is ambiguous (do they mean coat color, or coat type): specifically, the poodles which look white (other than albinos) are of the coat-hair-type "black", despite their white appearance.

To see a poodle of a COAT-HAIR-COLOR of "white" (no such thing) proves the existence of animals of a coat color type that violates all other observations of that animal, thus, increasing the probability that the same violation may apply to crows (which decreases the "probability that all crows are black") - thus making a case for a provably correct answer of "No".