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 AA and BB, then where they intersect represents ABA \cap B.

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 1,1,3,41, 1, 3, 4 and 0,2,2,50, 2, 2, 5. Find the probability of rolling both dice such that they add to 33.


Because 44 and 55 exceed 33, and we cannot roll negative numbers, it can be omitted in the sample space diagram.

++1\bm11\bm13\bm3
0\bm0111133
2\bm2333355
2\bm2333355

There are five 33s. But remember the full sample space has 4×4=164 \times 4 = 16 equal likely outcomes, so the probability is 516\frac{5}{16}\qed