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Question
Two different dice are thrown together. Find the probability of getting a total of 6 or 7 of the numbers on two dice.
Solution
When two dice are thrown simultaneously, the possible outcomes can be listed as follows:
| Outcome |
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) |
Total number of possible outcomes = 36
Outcomes where the numbers on the two dice total 6 = 5 [(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)]
Outcomes where the numbers on the two dice total 7 = 6 [(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)]
Number of favourable outcomes = 5 + 6 = 11
Thus, the probability of getting a total of 6 or 7 of the numbers on the two dice is `11/36`
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