Calculating probabilities
Here are two fair spinners. The total score is the sum of the two numbers the arrows point to.
Jot down, systematically, all the possible outcomes for the two spinners.
You will find it useful to use a table of results, as shown.
| Triangular spinner | Square spinner | Total score |
| 1 | 0 | 1 |
| 1 | 1 | 2 |
| 1 | 2 | 3 |
| 1 | 3 | 4 |
| 2 | 0 | 2 |
| 2 | 1 | 3 |
| 2 | 2 | 4 |
| 2 | 3 | 5 |
| 3 | 0 | 3 |
| 3 | 1 | 4 |
| 3 | 2 | 5 |
| 3 | 3 | 6 |
| Triangular spinner | 1 |
|---|---|
| Square spinner | 0 |
| Total score | 1 |
| Triangular spinner | 1 |
|---|---|
| Square spinner | 1 |
| Total score | 2 |
| Triangular spinner | 1 |
|---|---|
| Square spinner | 2 |
| Total score | 3 |
| Triangular spinner | 1 |
|---|---|
| Square spinner | 3 |
| Total score | 4 |
| Triangular spinner | 2 |
|---|---|
| Square spinner | 0 |
| Total score | 2 |
| Triangular spinner | 2 |
|---|---|
| Square spinner | 1 |
| Total score | 3 |
| Triangular spinner | 2 |
|---|---|
| Square spinner | 2 |
| Total score | 4 |
| Triangular spinner | 2 |
|---|---|
| Square spinner | 3 |
| Total score | 5 |
| Triangular spinner | 3 |
|---|---|
| Square spinner | 0 |
| Total score | 3 |
| Triangular spinner | 3 |
|---|---|
| Square spinner | 1 |
| Total score | 4 |
| Triangular spinner | 3 |
|---|---|
| Square spinner | 2 |
| Total score | 5 |
| Triangular spinner | 3 |
|---|---|
| Square spinner | 3 |
| Total score | 6 |
Use the table to answer these questions:
Question
How many different possible outcomes are there?
There are 12 possible outcomes.
All you have to do is count the number of entries in the table.
Question
How many outcomes gave a total score of 2?
Only 2 outcomes give a total score of 2: a '1' on each spinner, or a '2' on the triangular spinner and '0' on the square one.
Question
What is the probability of getting a total score of 2?
The number of outcomes giving a total score of 2 \(\div\) the total number of outcomes \(= \frac{2}{{12}}or\frac{1}{6}\)
Question
How many outcomes gave a total score of 4?
3 outcomes gave a total score of 4.
Question
What is the probability of getting a total score of 4?
The number of outcomes giving a total score of 4 \(\div\) the total number of outcomes \(= \frac{3}{{12}}or\frac{1}{4}\)
Relative frequency
You can estimate probabilities from an experiment. These are sometimes called experimental probabilities.
For example, in an experiment where you drop a drawing pin:
- the pin lands up 279 times
- the pin lands down 721 times
- the total number of throws is 1000
So the probability of the drawing pin landing up is:
The number of times this outcome occurs (pin up) \(\div\) total number of outcomes (or trials) \(= \frac{{279}}{{1000}}\,or\,0.279\,or\,27.9\%\)