Probability · Ordinary Level
Sample Space Grids
Ordinary Level · Class 6 · Tap NEXT to begin
Section 1 of 2
Two-Way Sample Spaces
List every pair
For two things happening together, list every pair. The total is (ways for the first) $\times$ (ways for the second).
Worked example — a coin and a die
A coin and a die are thrown. Find $P(\text{a tail and an even number})$.
$2 \times 6 = 12$ results: $T1,T2,T3,T4,T5,T6,H1,\ldots,H6$
Tail and even: $T2, T4, T6$
$P = \tfrac{3}{12} = \tfrac{1}{4}$
$\tfrac{3}{12} = \tfrac{1}{4}$
Worked example — two spinners
One spinner has $A, B, C, D$; another has $1, 2, 3$. Spin each once. Find $P(\text{an } A \text{ and an odd number})$.
$4 \times 3 = 12$ results: $A1,A2,A3,B1,\ldots,D3$
$A$ and odd: $A1, A3$
$P = \tfrac{2}{12} = \tfrac{1}{6}$
$\tfrac{2}{12} = \tfrac{1}{6}$
Section 2 of 2
Two Dice Added
Two dice are thrown and the results are added ($6 \times 6 = 36$ possible sums):
| + | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Worked example — a prime sum
Find $P(\text{a prime answer})$. (A prime has exactly two factors: itself and one — here $2, 3, 5, 7, 11$.)
Count the sums that are prime in the grid
$P = \tfrac{15}{36}$
$\tfrac{15}{36}$
You try
For the two dice added, find $P(\text{an answer of } 10 \text{ or more})$.
Count the cells showing $10$, $11$ or $12$.
$10$: three ways, $11$: two ways, $12$: one way $= 6$
$P = \tfrac{6}{36}$
$\tfrac{6}{36}$
That’s Class 6.
Two-way sample spaces and the two-dice grid. Class 7: tree diagrams.