complexity theory – Is the solution of a given boolean formula random?

I am curious because of P vs. NP

If you could show that it is random how many solutions to a boolean formula there are, would that prove P != NP because no algorithm can predict the random solutions then?

I know this question is poorly formulated and I am sorry if it got asked before. Maybe someone knows what my thoughts behind this are and could provide further explanation on why my intuition for this is wrong/right.