Positive bias refers to the human tendency to look for observations where a theory can explain, rather than making sure that observations that cannot be explained do not occur. In this case, it refers to Hermione coming up with number triplets that follow the particular rule, rather than trying to find any triplets that do not follow the rule, and would disconfirm her theory if they do.
Not to be confused with Confirmation bias .
The disclaimer is a reference to Arthur C. Clarke's novel 2010: Odyssey Two. The original quote is ALL THESE WORLDS ARE YOURS—EXCEPT EUROPA. ATTEMPT NO LANDINGS THERE.