Sample space diagrams
Sample space diagrams are usually listing out all the (equally-likely) outcomes in a grid or table, such as all the outcomes of rolling two dice. They can represent intersections more efficiently than venn diagrams.
For example if a row and a column represent and , then where they intersect represents .
Where there may not be time to construct a full sample space diagram, a partial one can be very useful to organize the information. They are essentially listing all (relevant) cases.
Example: Two fair four-sided dice have faces labeled and . Find the probability of rolling both dice such that they add to .
Because and exceed , and we cannot roll negative numbers, it can be omitted in the sample space diagram.
There are five s. But remember the full sample space has equal likely outcomes, so the probability is