Probability Diagrams

Laying out every outcome

• Where two experiments happen together, a table shows every combination in a grid
• The syllabus calls it a sample space diagram, and a question may print it as a table of the possible outcomes, sometimes partly filled in for you to complete
• Put one experiment along the top and the other down the side, then fill each cell with the combined result
• The number of cells is the total number of outcomes, and counting the cells that satisfy an event gives the numerator
• Complete the whole grid before counting, since a systematic table makes miscounting almost impossible
• A restricted question, such as "given that the total is odd", means counting only within the cells that meet the condition