My understanding is that events are subsets of the total outcomes in a sample space. So if two events are mutually exclusive, then they (the sets) do not overlap in the sample space. This can be seen graphically.
If events are independent, I understand it to mean that the occurrence of one does not affect the probability of the other occurring and vice versa and if events are dependent I understand that the occurrence of one affects the probability of another. So if we define $P(A)$ = $\frac{|A|}{|S|}$ where $A$ is the event and $S$ is the sample space so if events $A$ and $B$ are dependent, does that mean that the cardinalities of $A$ and $B$ have some relation to each other wherein one affects the other somehow? Shouldn't it be true since the cardinality of the sets directly determine the probability of the event? If true, would we be able to see these affects graphically when we talk about conditional probability?