I am confused about the concepts of:

independent events

mutually exclusive events

Positive and negative correlation of events

and how to represent them on Venn diagram.

Ok, I try to explain. Do correct me if I'm wrong.

2 events A and B can be disjoint (meaning they are mutually exclusive) or joint.

Venn {mutual exclusive} = 2 separate circles.

They are then negatively correlated, since the non-event of one will affect the occurance of another. In the extreme case, when A is the complement of B, the non-event of A means the occurance of B. So they cannot be independent events. Nor can they be positively correlated. They can only be negatively correlated.

As for

Venn {joint events} = 2 circles with interlocking region AnB in between.

They can then be negatively or positively correlated or correlation factor of 0, meaning independent events.

Dividing up the space into A,AnB and B,

To depict negatively correlation, we draw the area of AnB smaller than either A or B.

Extreme case is when AnB = 0 = mutually exclusive (mentioned earlier)

But how do we draw positive correlation?

And also how do we draw independent events? (Or we can't even depict it in Venn diagrams?)

Thanks!