| Event : 'Sum on 2 Dice' | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Probability |
1
36
|
5
36
|
12
36
|
Answer :
When two dice are rolled, total number of outcomes = (see the given table).
| - | 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 |
(i)
| Event : Sum on 2 dice | Favourable outcomes | No. of favourable outcomes | Probability =
No. of favourable outcomes
No. of total outcomes
|
|---|---|---|---|
| 2 | (1,1) | 1 |
1
|
| 3 | (1,2),(2,1) | 2 |
2
=
1
|
| 4 | (1,3),(2,2),(3,1) | 3 |
3
=
1
|
| 5 | (1,4),(2,3),(3,2),(4,1) | 4 |
4
=
1
|
| 6 | (1,5),(2,4),(3,3),(4,2),(5,1) | 5 |
5
|
| 7 | (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) | 6 |
6
=
1
|
| 8 | (2,6),(3,5),(4,4),(5,3),(6,2) | 5 |
5
|
| 9 | (3,6),(4,5),(5,4),(6,3) | 4 |
4
=
1
|
| 10 | (4,6),(5,5),(6,4) | 3 |
3
=
1
|
| 11 | (5,6),(6,5) | 2 |
2
=
1
|
| 12 | (6,6) | 1 |
1
|
(ii) The above (given) argument is wrong [from the above table].
The sum 2, 3, 4, ………… and 12 have different no. of favourable outcomes, moreover total number of outcomes are .