Question

20. Consider the experiment where one randomly rolls two die and the sums of the total number of dots. Provide a list of all possible outcomes and three examples of events.

Answer 1

List of all possible outcomes by rolling two dice

	1	2	3	4	5	6	Total
1	1 + 1 = 2	1 + 2 = 3	1 + 3 = 4	1 + 4 = 5	1 + 5 = 6	1 + 6 = 7	27
2	2 + 1 = 3	2 + 2 = 4	2 + 3 = 5	2 + 4 = 6	2 + 5 = 7	2 + 6 = 8	33
3	3 + 1 = 4	3 + 2 = 5	3 + 3 = 6	3 + 4 = 7	3 + 5 = 8	3 + 6 = 9	39
4	4 + 1 = 5	4 + 2 = 6	4 + 3 = 7	4 + 4 = 8	4 + 5 = 9	4 + 6 = 10	45
5	5 + 1 = 6	5 + 2 = 7	5 + 3 = 8	5 + 4 = 9	5 + 5 = 10	5 + 6 = 11	51
6	6 + 1 = 7	6 + 2 = 8	6 + 3 = 9	6 + 4 = 10	6 + 5 = 11	6 + 6 = 12	57
Total	27	33	39	45	51	57	252

Three examples of events

• sample event, where only one occurrence is possible i.e., 6+6, 1+1.
• compound events, where one total sum is possible in multiple ways i.e., 2+1, 1+2
• impossible events, where any number which is beyond the total number of dots on the die i.e., 7.