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The probability there are aliens is extremely high given the size of the Universe. But the probability there are intelligent aliens close enough, that survive long enough, that detect us or find us by accident (given again the size of the universe) and are advanced enough to come (or the other way us finding them)... well, I don't know, as far as we know it never happened. Everything is so far away !

As for the universe infinite or not, it's not proven, but it's a strong possibility. I read somewhere it should be at least 10 or 20 times bigger than what we can see given the current understanding. It would be quite "fun" if the universe is exactly the observable universe, that would make us at the exact middle of it !