Relative frequency and listing outcomes
Relative frequency
When you cannot work out a probability from equally likely outcomes, estimate it from an experiment: relative frequency = number of times it happened ÷ number of trials.
More trials give a more reliable estimate. If a fair coin gives 7 heads in 10 throws, that is not evidence of bias; 700 in 1000 would be.
Sample spaces
For two dice there are 6 × 6 = 36 equally likely outcomes.
Draw a grid of totals and count the ones you want: a total of 7 happens 6 ways, so P(7) = 6/36 = 1/6. The totals themselves are not equally likely, so never say P(7) = 1/11.
| + | 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 |
Counting choices: 4 starters and 5 mains give 4 × 5 = 20 different meals.
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