Sample Space Diagrams
Grade 3What is a sample space?
A sample space is just a complete list of every possible outcome. When two things happen at the same time — two coins, a dice and a spinner — it helps to draw them in a grid called a sample space diagram.
One event goes along the top, the other down the side. Each cell in the grid is one possible combined outcome. Count the cells to find your total.
Worked example — two dice
EXAMPLE
Two fair dice are rolled. Find (a) the total number of outcomes, (b) P(both dice show the same number), (c) P(the sum is 7).
Draw a 6 × 6 grid. The rows are dice 1 (1–6), columns are dice 2 (1–6).
(a) Total outcomes = 6 × 6 = 36.
(b) Matching pairs: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) — that's 6 cells. P(same) = 6/36 = 1/6.
(c) Pairs summing to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — that's 6 cells. P(sum = 7) = 6/36 = 1/6.
Reading probabilities from the grid
Once the grid is drawn, every probability question becomes a counting exercise. Circle or highlight the cells where your event happens, count them, then divide by the total number of cells.
Don't skip drawing the grid to save time — it's quicker to count from a grid than to try to list outcomes in your head and miss some.
