I am given that (strictly greater) and

I am to deduce whether B and C could be independent.

I am thinking no.

In order for the right side to be equal to this means at least

Now, since it was given that

, since this would make

Therefore

However implies and are not independent in this case because and ( since )

and not independent implies and aren't independent.

Is this sound reasoning? I am skeptical because this based of the converse of a true statement.

Thank you,

-Jame