The universe is random or chaotic?
Some of both, depending on your definitions.
Random means that the outcome can not be determined even with all information known. In the quantum world, there is plenty of that. Call that "strictly random". But most people would interpret "random" as being undetermined given what we can know. Call that "loosely random". That is a big difference and it leaves a lot of things in the universe categorized as "loosely random".
Chaotic means that the outcome is greatly affected by tiny differences (A butterfly flapping its wings in Brazil causing a hurricane.) There is a lot of that in the universe. Near collisions of planets are an example where a tiny difference in the fly-by conditions will put the resulting path on a completely different path. In that case, if we have perfect knowledge and calculation capability, we can figure out the result. So it is not what I would call "strictly random". But if we don't assume those perfect capabilities, we are in the "loosely random" category.
PS. I just made up the "strictly random" and "loosely random" terms. Someone may be able to give us a more formal answer to your question.
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