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 spaces?)

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