When the red dice shows '1', the yellow dice could show any one of the numbers 1, 2, 3, 4, 5, 6. The same is true when the red dice shows '2', '3', '4', '5' or '6'. The possible outcomes of the experiment are shown in the figure; the first number in each ordered pair is the number appearing on the red dice and the second number is that on the white dice.
| - | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 1,1 | 1,2 | 1,3 | 1,4 | 1,5 | 1,6 |
| 2 | 2,1 | 2,2 | 2,3 | 2,4 | 2,5 | 2,6 |
| 3 | 3,1 | 3,2 | 3,3 | 3,4 | 3,5 | 3,6 |
| 4 | 4,1 | 4,2 | 4,3 | 4,4 | 4,5 | 4,6 |
| 5 | 5,1 | 5,2 | 5,3 | 5,4 | 5,5 | 5,6 |
| 6 | 6,1 | 6,2 | 6,3 | 6,4 | 6,5 | 6,6 |
Note that the pair (1, 4) is different from (4, 1).
So, the number of possible outcomes n(S) =
(i) The outcomes favourable to the event 'the sum of the two numbers is 8' denoted by E,
i.e., the number of outcomes favourable to E is n(E) =
(ii) As there is no outcome favourable to the event F, 'the sum of two numbers is 13'
(iii) As all the outcomes are favourable to the event G, 'sum of two numbers is less than are equal to 12'