Foundation and Higher · sample spaces

Two dice?
Draw the grid.

36 outcomes,
all equally likely

a list of everything that could happen —

Sample space

two events: use a grid

one on top, one down the side

step 1 of 4

Build the grid

1. One dice on top, one down the side.

2. Fill each cell with the total.

✓ 6 × 6 = 36 equally likely outcomes

step 2 of 4

P(total is 7)

1. Circle every 7: they run in a diagonal.

2. There are 6 of them, out of 36.

✓ P(7) = 636 = 16

step 3 of 4

P(total more than 9)

1. More than 9 means 10, 11 or 12.

2. Count them: 3 + 2 + 1 = 6.

✓ P(more than 9) = 636 = 16

step 4 of 4

Any two events

1. 2 × 6 = 12 outcomes.

2. H2, H4, H6 fit: 3 of the 12.

✓ List or grid, then count

a coin and a dice

H1 H2 H3 H4 H5 H6

T1 T2 T3 T4 T5 T6

P(head and even) = 312 = 14

sample space —

Two events

draw a grid

Total outcomes

multiply: 6 × 6 = 36

Probability

count the cells that fit

The totals are not equally likely.
The 36 cells are.

The
Maths Habit

Download The Maths Habit app
to test your knowledge