Let $(S,P)$ be a (finite) probability space. We associate to $(S,P)$ a quantity $n(S,P)$ as follows:

The probability of two randomly chosen events $A,B\subset S$ being independent is denoted by $n(S,P)$

Is there a terminology for this quantity? Is it equivalent to some other well known terminology in probability theory?Can one generalize this concept to infinite sample spaces?(and a possible generalization to arbitrary measure space)?

What is this number for the experiment of rolling two different colored dice (the standard probability space this experiment generate)?