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 quantity for the sample space associated to the experiment of rolling two different colored dice (the standard probability space this experiment generates)?