Textbooks use Venn Diagrams to represent the probability space for two or more events. Venn Diagrams use circles, ovals or other irregular shapes to represent the probabilities of different events.

I prefer a variation on the Venn Diagram, in which the probabilities of individual events are represented by rectangles within the main box. With two events, A and B, the probability of A is represented by a rectangle along the left side of the box, and the probability of event B is represented by a rectangle along the bottom of the box.

The diagram shows that event A either occurs, with probability P(A), or it does not occur, with probability P(A^c). How would this be shown in a Venn diagram?

Here is the diagram for event B by itself.

Again, the sample space is simply {B,B^c}.

Now, we can use a Kling diagram to show two independent events, A and B. If they are independent, then P(A and B) = .15

The bottom left rectangle is what on a Venn Diagram would be shown as the intersection of the two events. However, in a Venn Diagram, I cannot think of any way to illustrate the fact that the events are independent. In the Kling Diagram, the events are independent because the probability of A (the width of the rectangles) is the same on top and bottom.

Next, suppose that A and B are positively related. Suppose that P(A and B) = .20, rather than .15. Then, we have

Compared with independent events, the probability of A is higher when B occurs (on the bottom) than otherwise (on the top).

Next, we have the Kling diagram for negatively related events.

Compared with independent events, the probability of A is lower when B occurs (on the bottom) than otherwise (on the top).