QUESTION 5
A fair die is thrown two times.
(a). Construct a table of the outcomes.
(b). Calculate the probability that the:
(i). sum of the outcomes is 8;
(ii). product of outcomes is less than 10;
(iii). outcomes contain at least a 3.
Observation
The Chief Examiner reported that this question was very popular among the candidates and their performance was commended. Majority of them were reported to obtain the following table of outcomes:
|
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 |
From the table, total number of outcomes = 36, number of outcomes whose sum was 8 = 5. Therefore, probability that the sum of the outcomes was 8 = 
= 
. The Outcomes whose product was less than 10 = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1), (6, 1)}. Number of outcomes whose product was less than 10 = 17. Therefore, probability that product of outcome was less than 10 = 
. Outcomes which contained at least a 3 = {(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3), (3, 1), (3, 2), (3, 4), (3, 5), (3, 6)}. Number of outcomes which contained at least a 3 = 11. Therefore, probability of at least a 3 = 
.