How come Wikipedia says that Random Turing Machines can provide uncomputable output?
It's not uncommon for Wikipedia to say dubious things.  Don't trust it as a primary reference.  Beware that hypercomputation is potentially a &quot;crank-adjacent&quot; subject, so the Wikipedia article on it might be especially at risk of containing material of uncertain reliability.  When you find something in Wikipedia you don't understand, my advice is to look at primary sources, such as good textbooks on the subject.
The statement &quot;the output of a random Turing machine is uncomputable&quot; does not look accurate to me.  It's not even clear to me what that would mean.  I'm not sure how computability would be defined for probabilistic machines -- that would need to be specified before such a statement can be assigned any truth value.
No, in computer science &quot;random&quot; does not mean the same thing as &quot;unknown&quot;.  In lay language &quot;random&quot; can mean &quot;arbitrary&quot; or &quot;I don't understand it&quot; or &quot;hard to predict&quot; or &quot;I don't know what's going on here&quot; or &quot;I don't see an obvious pattern&quot;, but in computer science &quot;random&quot; has a  specific technical meaning taken from probability theory.  See, e.g., https://cs.stackexchange.com/q/13893/755, https://cs.stackexchange.com/q/7729/755.