Why is intersection of two independent set probability a multiplication process? Why is the probability of intersection of two independent sets $A$ and $B$, a multiplication of their respective probabilities i.e. Why is
$$\mathbb{P}(A \cap B) = \mathbb{P}(A) \cdot \mathbb{P}(B)?$$
this question is about the intuition behind the definition of independence of sets in a probability space

hold two transparent sheets (A and B) on top of each other with an overlapping area C .
when we say intersection of A and B (sheet A independent of sheet B) it  means from every  'unique' part of sheet A ,overlapped by sheet B (CA) we can draw a 'unique' line to every part of sheet B ,over lapped by sheet A (CB). ...same goes when you say 5 * 6 you mean for every part of 5 there is all parts of 6 
