Interesting. I had never thought much about this before.
The word find can mean to reveal or discover. It's generally used as a transitive verb:
I think the scientists will find no correlation in the data.
My grandmother found an old purse in her attic.
The explorers walked along the coast, hoping to find a good harbor.
However, the word out can be added when we are talking about discovering a fact, or some information. In my three example sentences, this can easily be applied to the first one, like this:
Is there any correlation in the data? That's what the scientists want to find out.
The scientists want to find out if there is any correlation in the data.
That's why we can say:
My parents found out I came home late last night.
(they discovered the fact). However, we would NOT say:
The explorers hoped to find
out a good harbor.
My grandmother found
out an old purse in her attic.
Yet we COULD say:
My grandmother found out she had an old purse in her attic.
because that is talking about a fact, not a purse. Similarly:
The explorers found out there was no good harbor on the coastline.
is okay, but when we change this from talking about a fact to talking about a harbor, we say:
The explorers found no good harbor on the coastline.
with no "out" used.