The sample space consists of all possible combinations of the numbers rolled on the two dice. We can represent this using a table:
| | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
For example, if we roll a 1 and a 4, the sum is 5.
To count the number of 8's, we simply count the number of pairs of dice that sum to 8. We can see that there are 5 such pairs: (2,6), (3,5), (4,4), (5,3), and (6,2). Therefore, the answer is B) 55.
List the sample space for rolling two dice and finding the sum of the numbers. How many 8's are there in the sample space? [Assume that rolling a 3 and a 5 is the same as rolling a 5 and a 3.]
Responses
A 33
B 55
C 22
D 4
1 answer