When do we need an alternative explanation for statistically unlikely events?
I ask because I am interested in miracles: is an extremely unlikely event enough to warrant the claim that something is out of the ordinary and we need a new explanation for it, which seems necessary for miracle claims.
If not, they may be reserved for facts that go against our natural understanding of the world (resurrection of the dead, statues bleeding, etc.), and then even the most unlikely results, being nomologically possible, are never miracles.
I'm guessing (being no sort of scientist) the answer might involve statistical variation, and wether we ever infer scientifically etc. than events with a vanishingly small probability are actually "impossible". Do we? Just two, slightly different, examples
- is it scientifically possible e.g. for a man to be 30 feet tall?
- do we need to a new explanation for me winning the lotto 1000 days in a row, beyond me buying tickets?
If so, what is extremely unlikely is not already accounted for, then an extremely low probability may signal something is nomologically impossible and a miracle if it does occur. If not, then its freakish unlikelihood does not make it a candidate for miracle claims.