ANATOMY OF A VENN DIAGRAM SAMPLE SPACE Just as graphs are useful in describing sets of data, a pictorial method for presenting a sample space and events can often be useful for explaining and understanding probability. Although almost any shape can be used, we most often use a rectangle to represent the sample space, and circles within the rectangle to represent events. EVENT A EVENT B As a simple example, let us consider a group of six students, Tom, Bill, Cathy, Theresa, Corinne, and Jim. Theresa, Corinne, Jim, and Bill are studying Spanish. Tom and Cathy are studying French. Consider the Sample Space to represent all languages. If we let Event A denote “studying Spanish,” and Event B denote “studying French,” a Venn Diagram representing this would appear as: Now let us suppose that after a day or so, Bill has had it with Spanish, and decides that maybe Greek is his “language of choice.” A Venn Diagram representing this situation would appear as: Finally, let us suppose that two new students join the group. Tyler and Sue are studying both Spanish and French. A Venn Diagram representing this situation would appear as: A B A B A B Jim Theresa Corinne Tom Cathy Jim Bill Theresa Corinne Jim Theresa Corinne Tyler Sue Tom Cathy Tom Cathy Bill Bill Note that these are just the simplest of Venn Diagrams. The diagrams can contain many events (circles), with some or all of them overlapping.